Geometry Skills
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Foundations
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Vocabulary
- Determine definitions of undefined terms of geometry, fill in the blank
- Determine definitions of angles & shapes, fill in the blank
- Determine definitions of conjectures, fill in the blank
- Determine definitions of theorems, fill in the blank
- Determine definitions of postulates, fill in the blank
- Condensed: Determine definitions of general geometry vocabulary, fill in the blank
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Points, Lines, & Angles
- Identify angles, lines, & segments in figures
- Identify characteristics of points, lines, segments & rays from diagrams
- Identify characteristics of points, lines, segments & rays from descriptions
- Condensed: Identify characteristics of points, lines, segments & rays
- Given geometric figure, identify correct conjecture
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Spherical & Euclidean Geometry
- Identify properties of spherical geometry
- Identify properties of Euclidean & spherical geometry
- Identify triangle angle sums in Euclidean & spherical geometry
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Distance, Midpoint, & Segment Addition Postulate
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Distance
- Determine distance between two points on number line
- Determine fractional distance between two points on number line
- Determine distance between points
- Determine distance between points, horizontal or vertical
- Given segment on coordinate plane, determine length
- Determine distance between points, including coordinate plane
- Determine fractional distance or fractional point dividing segment into specified ratio
- Given coordinates for vertices of triangle, determine length of sides
- Given coordinates, use length to determine segment congruence
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Midpoint
- Determine midpoint of segment on number line
- Given endpoints, determine midpoint
- Determine midpoint of two points on coordinate plane
- Given midpoint & endpoint, determine other endpoint on coordinate plane
- Condensed: Determine midpoint or endpoint of segment on coordinate plane
- Determine point that divides segment into specified ratio on coordinate plane
- Given endpoint & point dividing segment into specified ratio, determine other endpoint on coordinate plane
- Condensed: Determine endpoint or point dividing segment into specified ratio on coordinate plane
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Distance & Midpoint
- Given midpoint or distance between points, determine missing endpoint
- Condensed: Determine distance or midpoint on number line
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Segment Addition Postulate
- Apply segment addition postulate
- Apply segment addition postulate, algebraic expressions
- Given midpoint, apply segment addition postulate, algebraic expressions
- Condensed: Apply segment addition postulate, including algebraic expressions
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Logical Reasoning
- Determine truth values of conditionals or identify counterexamples
- Given conditional, determine converse & its truth value
- Given conditional, determine inverse & its truth value
- Given conditional, determine contrapositive & its truth value
- Given conditional, determine biconditional
- Condensed: Determine conditional statements, counterexamples, & truth values
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Angles
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Classifying Angles
- Classify angles from figure
- Identify angle names
- Identify angle pairs
- Identify types of angles in figures
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Measuring Angles
- Estimate angle measures
- Identify 90°, 180°, 270°, & 360° angles
- Identify angles with specified measures
- Measure angles using protractor
- Measure angles using protractor, real-world context
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Angle Addition Postulate
- Apply angle addition postulate to determine angle measures
- Apply angle addition postulate to determine angle measures, algebraic expressions
- Condensed: Apply angle addition postulate to determine angle measures, including algebraic expressions
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Angle Pairs
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Vertical Angles
- Given vertical angles, determine angle measure
- Given vertical angles, determine angle measure, one algebraic expression
- Given vertical angles, determine angle measure, multiple algebraic expressions
- Given parallel lines with transversal & angle, determine vertical angle
- Given parallel lines with transversal & angle, determine vertical angle, algebraic expressions
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Complementary Angles
- Given complementary angles, determine angle measure
- Given complementary angles, determine angle measure, one algebraic expression
- Given complementary angles, determine angle measure, multiple algebraic expressions
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Supplementary Angles
- Given supplementary angles, determine angle measure
- Given supplementary angles, determine angle measure, one algebraic expression
- Given supplementary angles, determine angle measure, multiple algebraic expressions
- Given vertical angles, determine supplementary angle measure
- Given vertical angles, determine supplementary angle measure, algebraic expressions
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Complementary & Supplementary Angles
- Determine complementary, supplementary, or equivalent angle measures
- Determine complementary, supplementary, or equivalent angle measures, algebraic expressions
- Given vertical, complementary, or supplementary angles, determine angle measure, one algebraic expression
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Transversals
- Determine & identify classification of angle pairs
- Given parallel lines with transversal, identify specified angle pairs, only numbered angles, uses “consecutive” terminology
- Given parallel lines with transversal & angle, identify specified angle pairs, uses “consecutive” terminology
- Given parallel lines with transversal, identify specified angle pairs, only numbered angles, uses “same-side interior” terminology
- Given parallel lines with transversal & angles, identify specified angle pairs, uses “same-side interior” terminology
- Given parallel lines with transversal & angle, determine & justify specified angle
- Given three parallel lines with two transversals, determine lengths
- Given non-parallel lines & transversal, identify transversal & specified angle pairs
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Alternate Interior & Alternate Exterior Angles
- Given parallel lines with transversal & angle, determine alternate interior angle
- Given parallel lines with transversal & angle, determine alternate exterior angle
- Given parallel lines with transversal & angle, determine alternate interior angle, algebraic expressions
- Given parallel lines with transversal & angle, determine alternate exterior angle, algebraic expressions
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Corresponding & Same-Side Interior Angles
- Given parallel lines with transversal & angle, determine corresponding angle
- Given parallel lines with transversal & angle, determine same-side interior angle
- Given parallel lines with transversal & angle, determine corresponding angle, algebraic expressions
- Given parallel lines with transversal & angle, determine same-side interior angle, algebraic expressions
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Mixed Angle Pairs
- Determine angle measures, including figures or descriptions
- Determine angle measures in figures
- Determine angle measures in figures, algebraic expressions
- Determine angle measures in figures, two algebraic expressions
- Determine angle measures in figures, up to two algebraic expressions
- Determine angle measures involving parallel lines, algebraic expressions
- Determine angle measures involving parallel lines, algebraic expressions
- Given parallel lines with transversal & angle, determine supplement to corresponding angle
- Given parallel lines with transversal & angle, determine supplement to corresponding angle, algebraic expressions
- Given parallel lines with transversal & angle, determine specified angle, algebraic expressions
- Given parallel lines with transversal & angle, apply converse angle theorems, including algebraic expressions
- Given parallel lines with transversal & angle, determine specified angle
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Parallel & Perpendicular Lines
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Equations of Parallel & Perpendicular Lines
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Parallel or Perpendicular to an Axis
- Determine equation of line through specified point parallel or perpendicular to x-axis
- Determine equation of line through specified point parallel or perpendicular to y-axis
- Condensed: Determine equation of line through specified point parallel or perpendicular to x- or y-axis
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Two Points or Graph
- Identify equation that is parallel or perpendicular to line through two given points
- Given two points for one line, determine equation for parallel or perpendicular line through specified point
- Given graph of line, determine equation for parallel or perpendicular line through specified point
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Equations in Slope-Intercept Form or Standard Form
- Given two slope-intercept form equations, identify as parallel or perpendicular
- Given two equations in standard form, identify as parallel or perpendicular
- Given slope & point, determine equation for parallel or perpendicular line through specified point
- Given equation in slope-intercept form, determine equation of parallel line through specified point
- Given equation in slope-intercept form, determine equation of perpendicular line through specified point
- Given equation in slope-intercept form, determine equation of parallel or perpendicular line through specified point
- Condensed: Determine equations for parallel & perpendicular lines through specified points
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Equations in Mixed Forms
- Given equation in various forms, determine equation of parallel line through specified point
- Given equation in various forms, determine equation of perpendicular line through specified point
- Given equation in various forms, determine equation of parallel or perpendicular line through specified point
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Identifying Parallel, Perpendicular, & Intersecting LInes
- Identify intersecting lines in figures, real-world context
- Identify parallel & perpendicular lines in figures, real-world context
- Identify parallel & perpendicular lines in figures
- Condensed: Identify types of lines in figures, real-world context
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Congruence
- Determine missing steps in proofs involving angles
- Determine missing steps in proofs involving segments
- Determine missing steps in proofs involving parallel lines
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Triangles
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Classifying Triangles
- Classify triangles by sides
- Classify triangles by angles
- Classify triangle based on given angle measures
- Classify triangles based on angles & sides
- Apply triangle inequality theorem to determine side lengths
- Apply triangle inequality theorem to determine range of values for unknown side
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Triangle Angle Sum & Exterior Angles Theorems
- Given two angle measures in triangle, determine angle measure
- Given two angle measures in triangle, determine & justify angle measure
- Apply triangle angle sum theorem to determine angles, algebraic expressions
- Apply triangle angle sum theorem to determine appropriate equation & angles, algebraic expressions
- Apply triangle angle sum theorem to determine angles, multiple algebraic expressions
- Given description, apply triangle angle sum theorem to determine angles, algebraic expressions
- Apply triangle exterior angle theorem to determine angles, including algebraic expressions
- Condensed: Apply triangle angle sum theorem & exterior angle theorem to determine angles, including algebraic expressions
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Angle-Side Relationships
- Order angles in triangles
- Determine smallest & largest sides or angles in triangle
- Determine angles & order side lengths in triangles, algebraic expressions
- Condensed: Determine angles & order side lengths & angles in triangles, including algebraic expressions
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Perpendicular & Angle Bisectors
- Given perpendicular bisector in triangle, determine segment lengths
- Given perpendicular bisector in triangle, determine segment lengths, algebraic expressions
- Given angle bisector in triangle, determine angles
- Given angle bisector in triangle, determine angles, algebraic expressions
- Determine segment lengths in triangles with angle bisectors
- Condensed: Given perpendicular or angle bisector in triangle, determine segment lengths or angles, including algebraic expressions
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Isosceles & Equilateral Triangles
- Given congruent sides, identify congruent angles of isosceles triangle
- Given congruent angles, identify congruent sides of isosceles triangle
- Solve problems involving perimeter of equilateral triangles
- Solve problems involving perimeter of isosceles triangles
- Given equilateral triangle & algebraic expressions for sides, solve for variable or determine side length
- Given equilateral triangle & algebraic expression for angle, solve for variable
- Determine angle measure in isosceles triangle, at most one algebraic expression
- Determine angle measure in isosceles triangle, up to two algebraic expressions
- Condensed: Solve problems involving perimeter of equilateral & isosceles triangles
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Midsegment & Hinge Theorems
- Apply triangle midsegment theorem to determine segment lengths
- Apply triangle midsegment theorem to determine segment lengths, algebraic expressions
- Apply triangle midsegment theorem to determine perimeter
- Apply hinge theorem
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Geometric Mean
- Apply geometric mean to determine altitude
- Apply geometric mean to determine length with specified altitude
- Apply geometric mean to determine length of longer part of hypotenuse
- Apply geometric mean to determine length of shorter part of hypotenuse
- Apply geometric mean to determine shorter leg of triangle
- Apply geometric mean & quadratic equations to determine length of shorter part of hypotenuse
- Apply geometric mean to determine longer leg of triangle
- Apply geometric mean & quadratic equations to determine length of longer part of hypotenuse
- Apply geometric mean to determine length of segment of hypotenuse, legs given
- Apply geometric mean to determine lengths
- Apply geometric mean & quadratic equations to determine length of part of hypotenuse
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Medians & Centroids
- Given median of triangle, determine variable or length of bisected side, algebraic expressions
- Apply centroid theorem
- Determine coordinates of centroid of triangles
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Equations of Triangle Segments
- Determine equations for medians of triangles
- Determine equations for altitudes of triangles
- Determine equations for midsegments of triangles
- Determine equations for perpendicular bisectors of triangles
- Condensed: Determine equations for segments of triangles
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Triangle Similarity & Congruence
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Similar Triangles
- Identify corresponding parts of similar figures
- Determine similarity of triangles using AA similarity
- Determine angles of similar triangles using AA similarity
- Determine similar triangles using SAS similarity
- Determine similar triangles using SSS similarity
- Determine missing steps in proofs involving similar triangles
- Determine missing steps in proofs involving similar triangles, paragraph form
- Determine sides of similar triangles using AA similarity
- Determine angles of similar triangles using AA similarity, algebraic expressions
- Condensed: Determine similar triangles using SAS or SSS similarity
- Determine segment lengths using triangle proportionality theorem
- Determine dimensions using similar figures & indirect measurements
- Given right triangle with altitude from right angle, identify similar triangles
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Proofs
- Determine missing steps in proofs involving SSS in triangles
- Determine missing steps in proofs involving SAS in triangles
- Determine missing steps in proofs involving ASA in triangles
- Determine missing steps in proofs involving AAS in triangles
- Determine missing steps in proofs involving triangle congruence theorems
- Determine missing steps in proofs involving triangle congruence theorems, paragraph form
- Determine missing steps in proofs involving corresponding parts
- Determine missing steps in proofs involving corresponding parts, paragraph form
- Apply triangle theorems or determine missing steps in proofs
- Condensed: Determine missing steps in paragraph form proofs
- Given congruent triangles, determine values from corresponding parts
- Determine missing steps in proofs involving quadrilaterals
- Determine missing steps in proofs involving quadrilaterals, paragraph form
- Determine missing steps in proofs involving triangles
- Determine missing steps in proofs involving isosceles triangles
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Right Triangles & Trigonometry
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Basic Right Triangles & Pythagorean Theorem
- Given three sides, classify triangles
- Classify triangles using Pythagorean inequality theorem
- Given legs, determine hypotenuse
- Given two sides, determine missing side of right triangle
- Given leg & hypotenuse of right triangle, determine other leg
- Given triangle with algebraic expressions, apply Pythagorean theorem to determine side
- Determine Pythagorean triples
- Apply converse of Pythagorean theorem
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Application of Right Triangles & Pythagorean Theorem
- Given Pythagorean theorem model, determine specified component
- Solve problems using Pythagorean theorem, figure included, real-world context
- Given two sides, determine missing side of right triangle, real-world context
- Solve problems using Pythagorean theorem, real-world context
- Given ratio of sides & one dimension, apply Pythagorean theorem to determine specified dimension, real-world context
- Determine side of right triangle or apply converse of Pythagorean theorem, including real-world context
- Apply Pythagorean theorem to find length in kite
- Given segment on coordinate plane, determine length
- Determine area of triangles using sine formula
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Special Right Triangles
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30-60-90 Triangles
- Given 30-60-90 triangle, determine side
- Given 30-60-90 triangle & short leg, determine hypotenuse
- Given 30-60-90 triangle & long leg, determine short leg
- Given 30-60-90 triangle & short leg, determine long leg
- Given 30-60-90 triangle & long leg, determine hypotenuse
- Given 30-60-90 triangle & hypotenuse, determine short leg
- Given 30-60-90 triangle & hypotenuse, determine long leg
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45-45-90 Triangles
- Given 45-45-90 triangle, determine hypotenuse
- Given 45-45-90 triangle, determine leg
- Given 45-45-90 triangle, determine side
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Application of Special Right Triangles
- Condensed: Given special right triangle, determine side
- Determine angles using special right triangle relationships, real-world context
- Determine sides using special right triangle relationships, real-world context
- Condensed: Determine angles or sides using special right triangle relationships, real-world context
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Evaluate Right Triangles
- Given sine, cosine, or tangent & quadrant, determine trig function values
- Determine trig function values, degrees, calculator expected
- Determine trig function values, radians, calculator expected
- Condensed: Determine trig function values, calculator expected
- Condensed: Given special right triangle, determine trig function value
- Given right triangle, determine missing side & trig ratio, sin, cos, & tan
- Given right triangle, determine missing side & trig ratio, cot, sec, & csc
- Identify definitions of trig functions
- Condensed: Given right triangle, determine missing side & trig ratio
- Determine relationship between trig ratios of sides of similar triangles, sin, cos, & tan
- Given right triangle, determine trig ratio, sin, cos, & tan
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Law of Sines & Law of Cosines
- Determine sides of triangles using law of sines
- Determine sides of triangles using law of cosines
- Determine angles of triangles using law of cosines
- Determine sides or angles of triangles using law of cosines, multiple choice
- Condensed: Determine sides & angles of triangles using law of cosines
- Determine sides & angles of triangles using law of sines, real-world context
- Determine sides & angles of triangles using law of cosines, real-world context
- Condensed: Determine sides & angles of triangles using law of sines or law of cosines, real-world context
- Determine angles of triangles using law of sines
- Condensed: Determine sides & angles of triangles using law of sines
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Quadrilateral Properties
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Rectangle Properties
- Determine angle measures in rectangles with diagonals
- Given diagonals with algebraic expressions in rectangle, determine variable or diagonal length
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Parallelogram Properties
- Given parallelogram with algebraic expressions for opposite angles, determine angle measure
- Given parallelogram with algebraic expressions for opposite sides, solve for variable or side length
- Determine angle measures in parallelograms, including diagonals
- Given algebraic expressions for segments of diagonals in parallelogram, solve for variable or determine diagonal length
- Given parallelogram or parallel lines, identify consecutive angles or determine angle measure, algebraic expressions
- Identify or determine parallelograms in coordinate plane
- Given three points, determine fourth point to make parallelogram
- Condensed: Given parallelogram, determine sides & angles, including diagonals
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Trapezoid Properties
- Determine angle measures in trapezoids, including diagonals
- Determine angle measures in isosceles trapezoid, using congruent base angles
- Determine angle measures in isosceles trapezoid, using supplementary angles
- Determine diagonal lengths in isosceles trapezoids with algebraic expressions
- Determine segment length using trapezoid midsegment theorem
- Condensed: Given trapezoid, determine lengths or angle measures, including diagonals
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Rhombus Properties
- Determine angle measures in rhombus, including diagonals
- Determine angle measures in rhombus with diagonals, using perpendicular relationship
- Determine angle measures in rhombus with diagonals, using bisected opposite angles
- Condensed: Given rhombus, determine angle measures, including diagonals
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Kite Properties
- Identify congruent angles or determine angle measures in kites, algebraic expressions
- Given lengths of diagonals in kite, determine sides or perimeter
- Apply Pythagorean theorem to find length in kite
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Mixed Quadrilateral Properties & Proofs
- Identify properties of quadrilaterals
- Given quadrilateral in coordinate plane, determine equation of side based on slope of opposite side
- Determine missing steps in proofs involving quadrilaterals
- Determine missing steps in proofs involving quadrilaterals, paragraph form
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Polygons
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Polygon Properties & Theorems
- Identify properties of polygons
- Determine interior angles or sum of angles in polygons
- Determine interior angles or sum of angles in polygons, algebraic expressions
- Determine exterior angles or number of sides in polygons
- Determine exterior angles or sum of angles in polygons, algebraic expressions
- Condensed: Determine interior angles, exterior angles, or angle sum of polygons, including algebraic expressions
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Polygon Congruence
- Identify corresponding parts from congruence statement or determine congruence statement from figures
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Classifying 2D & 3D Figures
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Classifying 2D Figures
- Classify polygons based on number of sides or relationship to other shapes
- Classify polygons using graphic organizers, including types of triangles
- Classify polygons using graphic organizers
- Classify quadrilaterals shapes based on attributes
- Classify polygons based on angles & parallel or perpendicular lines
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Classifying 3D Figures
- Identify 3D figures & their bases
- Determine cross sections of cylinders
- Determine cross sections of prisms
- Determine cross sections of pyramids
- Determine cross sections of 3D figures
- Determine 3D figures from rotations of 2D figures
- Condensed: Determine cross sections of cylinders, pyramids, & cones
- Identify equivalent representations of 3D figures & nets
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Perimeter & Area
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Rectangle Perimeter & Area
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Rectangle Perimeter
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Basic Recatangle & Square Perimeter
- Determine perimeter of rectangles
- Given sides of rectangle, determine perimeter
- Given perimeter & one dimension of rectangle, determine missing dimension
- Given perimeter & relationship between sides, determine specific dimension
- Given perimeter of rectangle & one side, determine dimension
- Determine algebraic expressions for perimeter of rectangles
- Determine perimeter of rectangles, including decimal dimensions
- Given perimeter of rectangle & one side, determine dimension, including decimals
- Determine perimeter of composite figures containing rectangles & squares, including real-world context
- Condensed: Determine perimeter of rectangles, including real-world context
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Application of Rectangle & Square Permimeter
- Given sides of rectangle, determine perimeter
- Determine perimeter of rectangles, real-world context
- Determine perimeter of rectangles, including decimal dimensions, real-world context
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Modeling Rectangle & Square Perimeter
- Given model, identify formula & determine perimeter of rectangles
- Given model, identify formula & determine perimeter of rectangles, including decimal dimensions
- Determine side length or perimeter of squares
- Condensed: Identify formula & determine perimeter of rectangles & squares
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Rectangle Area
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Basic Rectangle & Square Area
- Given sides of rectangle, determine area
- Given length & width of rectangle, determine area
- Given area of rectangle & one dimension, determine other dimension
- Given area & one dimension of rectangle, determine missing dimension
- Determine area of rectangles with fractional dimensions
- Determine algebraic expressions for area of rectangles
- Determine area of rectangles with fractional dimensions using tiling method
- Given area of square, estimate side length
- Condensed: Determine area of rectangles, including real-world context
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Application of Rectangle & Square Area
- Determine area of missing dimension of rectangles, real-world context
- Determine equations that represent area of rectangles, real-world context
- Given sides of rectangle & cost per square unit, determine area & total cost, real-world context
- Determine area of shaded region between nested rectangles
- Determine algebraic expressions for area of shaded region between two nested rectangles
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Modeling Rectangle & Square Area
- Given model, identify formula & determine area of rectangle
- Given model, identify formula & determine area of square
- Condensed: Given model, identify formula & determine area of square or rectangle
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Rectangle Mixed Perimeter & Area
- Determine dimension of rectangles, including real-world context
- Determine dimensions that maximize area of rectangle for given perimeter
- Condensed: Identify formula & determine perimeter or area of rectangles & squares
- Condensed: Determine area & perimeter of rectangles, including real-world context
- Condensed: Determine algebraic expressions for perimeter or area of rectangles
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Parallelogram Perimeter & Area
- Determine area of parallelograms using models that decompose & rearrange parts
- Determine equations that represent area of parallelograms, real-world context
- Determine area of parallelograms
- Determine area or perimeter of parallelograms
- Given area & one dimension of parallelogram, determine missing dimension
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Triangle Area
- Determine area of triangles using models that decompose & rearrange parts
- Determine area of triangles
- Determine area of triangles, mixed numbers
- Determine area of triangles, internal height
- Determine area of triangles, internal height, mixed numbers
- Determine area of triangles, external height
- Determine area of triangles, external height, mixed numbers
- Given area & one dimension of triangle, determine missing dimension
- Given area & one dimension of triangle, determine missing dimension, mixed numbers
- Determine equations that represent area of triangles, real-world context
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Trapezoid Area
- Determine area of trapezoids using models that decompose & rearrange parts
- Determine area of trapezoids
- Given area & base lengths of trapezoid, determine height
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Circle Area & Circumference
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Circle Circumference
- Determine circumference of circle, exact answers, multiple choice, including real-world context
- Given radius or diameter, determine circumference
- Given circumference of circle, determine radius or diameter
- Estimate diameter or circumference & identify equations using π
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Circle Area
- Given radius or diameter, determine area
- Determine area of circle, exact answers, including real-world context
- Determine areas of semicircles & quarter circles
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Circle Mixed Area & Circumference
- Given radius or diameter, determine area or circumference
- Identify approximate formulas for circumference & area of circles
- Condensed: Determine area or circumference of circle
- Condensed: Given area or circumference of circle, determine radius or diameter
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Polygon Perimeter & Area
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Polygon Perimeter
- Determine perimeter of polygons, including real-world context
- Given coordinates of vertices, determine side lengths & perimeter of polygons
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Polygon Area
- Determine area of polygons in coordinate plane
- Determine area of polygons in coordinate plane, real-world context
- Determine apothem, area, or side length of regular triangle
- Determine apothem, area, or side length of regular pentagon
- Determine apothem, area, or side length of regular heptagon
- Determine apothem, area, or side length of regular hexagon
- Determine apothem, area, or side length of regular octagon
- Condensed: Determine apothem, area, or side length of regular polygon
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Mixed Figure Perimeter & Area
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Mixed Figure Area
- Condensed: Determine area using models that decompose & rearrange parts
- Determine areas of rectangles & parallelograms
- Given area, determine dimensions of rectangles & parallelograms
- Condensed: Determine areas & dimensions of rectangles & parallelograms
- Determine areas of triangles & trapezoids
- Given area, determine dimensions of triangles
- Condensed: Determine areas & dimensions of triangles & trapezoids
- Determine algebraic expressions that represent area of rectangles & triangles
- Determine area of shaded region between nested shapes
- Condensed: Determine equations that represent area of triangles & quadrilaterals, real-world context
- Given coordinates of vertices, determine area of triangle or rectangle
- Determine area of polygons in coordinate plane
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Mixed Figure Formulas & Applications
- Identify formulas for area & perimeter of basic shapes
- Determine dimensions that maximize area of rectangle for given perimeter
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Composite Figure Perimeter & Area
- Determine perimeter of composite figures containing rectangles & squares, including real-world context
- Determine algebraic expressions that represent area of rectangles & triangles
- Determine area of composite figures, no circular shapes
- Determine area of composite figures on coordinate plane, no circular shapes
- Determine area of composite figures, rectangle with various figures attached, no circular parts
- Determine area of composite figures, rectangle with various figures attached
- Determine area of composite figures, at least three subdivisions
- Determine area of composite figures
- Determine area of composite figures, real-world context
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Area of Shaded Region
- Determine area of shaded region between nested rectangles
- Determine area of shaded region between nested shapes
- Determine algebraic expressions for area of shaded region between two nested rectangles
- Determine probabilities from shaded areas of geometric figures, real-world context
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Surface Area & Volume
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Mixed Figures Surface Area Given Nets
- Identify equivalent representations of 3D figures & nets
- Given net, determine surface area of rectangular prism
- Given net, determine lateral surface area of prisms
- Given net, determine surface area of rectangular & triangular prisms & pyramids
- Given net, determine surface area of prisms
- Given net, determine surface area of pyramids
- Given net, determine surface area of prisms & pyramids
- Given net, determine lateral surface area of pyramids
- Given net, determine lateral surface area of prisms & pyramids, real-world context
- Condensed: Given net, determine surface area & lateral surface area of prisms & pyramids, including real-world context
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Cube Surface Area & Volume
- Determine 2D orthographic representation of 3D blocks
- Determine volume of cubes, whole numbers or decimals
- Determine volume of cubes, whole numbers, decimals, or fractions
- Determine volume of cubes, whole numbers, decimals, or fractions, no visual provided
- Determine volume of cubes, whole numbers or decimals, real-world context
- Determine volume of cubes, whole numbers, decimals, or fractions, real-world context
- Given volume, determine side length of cubes, whole numbers, decimals, or fractions
- Condensed: Determine volume or side length of cubes, whole numbers, decimals, or fractions, including real-world context
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Rectangular Prism Surface Area & Volume
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Rectangular Prism Volume Using Unit Cubes
- Determine relationship between area, volume, square units, & cubic units
- Determine relationship between area, volume, & dimensions
- Determine volume of rectangular prisms using unit cubes
- Determine volume of rectangular prisms using unit cubes
- Determine volume of rectangular prisms using repeated layers of base area, real-world context
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Basic Rectangular Prism Volume & Surface Area
- Determine surface area of rectangular prisms
- Interpret volume of rectangular prisms, various representations
- Determine volume of rectangular prisms, various representations
- Determine volume of rectangular prisms, whole numbers or decimals
- Determine volume of rectangular prisms, whole numbers or decimals
- Determine volumes of rectangular prisms, fractional dimensions
- Determine volume of rectangular prisms, whole numbers, decimals, or fractions
- Given base area & edge or all edges, determine volume of rectangular prism
- Determine volume or edge of rectangular prisms, whole numbers
- Given volume, determine edges of rectangular prisms
- Given volume, determine dimension of rectangular prism, fractional dimensions
- Condensed: Determine volume or dimension of rectangular prisms, fractional dimensions
- Condensed: Determine volumes or edges of rectangular prisms, whole numbers, decimals, or fractions, including real-world context
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Application of Rectangular Prism Volume
- Determine equations for volume of rectangular prisms, rational dimensions, real-world context
- Determine volume of rectangular prisms using various representations of cubic units, real-world context
- Determine volumes of rectangular prisms, rational dimensions, real-world context
- Determine volume of rectangular prisms & apply associative property to volume expressions
- Determine volume or edge of rectangular prisms, whole numbers or decimals, real-world context
- Determine volume of rectangular prisms, whole numbers, including real-world context
- Determine volume or edge of rectangular prisms, whole numbers, decimals, or fractions, real-world context
- Condensed: Determine volumes or edges of rectangular prisms, whole numbers, decimals, or fractions, including real-world context
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Triangular Prism Surface Area
- Determine surface area of triangular prisms
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Sphere Surface Area & Volume
- Determine volume of spheres
- Determine volume or radius of spheres
- Given volume, determine radius, diameter, or surface area of sphere
- Determine surface area of spheres
- Given surface area, determine radius, diameter, or volume of sphere
- Condensed: Given surface area or volume, determine dimension of sphere
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Cylinder Surface Area & Volume
- Determine volume of cylinders
- Given base area & height, determine volume of cylinder
- Given volume, determine dimension of cylinder
- Determine surface area of cylinders
- Given surface area, determine dimension of cylinder
- Determine lateral surface area of cylinders
- Condensed: Given surface area or volume, determine dimension of cylinder
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Cone Surface Area & Volume
- Determine volume of cones
- Given volume, determine dimension of cone
- Determine surface area of cones
- Given surface area, determine dimension of cone
- Determine lateral surface area of cones
- Condensed: Given surface area or volume, determine dimension of cone
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Pyramid Surface Area & Volume
- Determine volume of pyramids
- Given volume, determine dimension of pyramid
- Determine surface area of pyramids
- Determine surface area of pyramids
- Given surface area, determine dimension of pyramid
- Given net, determine surface area of pyramids
- Given net, determine lateral surface area of pyramids
- Determine lateral surface area of pyramids
- Condensed: Given surface area or volume, determine dimension of pyramid
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Composite Figure Surface Area & Volulme
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Composite Figure Surface Area
- Determine surface area of composite figures, rectangular & triangular prisms
- Determine surface area of composite figures, cylinders & cones
- Determine surface area of composite figures, cylinders & hemispheres
- Determine surface area of composite figures, prisms & pyramids
- Determine lateral surface area of composite figures, rectangular & triangular prisms
- Determine lateral surface area of composite figures, cylinders & cones
- Determine lateral surface area of composite figures, cylinders & hemispheres
- Determine lateral surface area of composite figures, prisms & pyramids
- Condensed: Determine total surface area & lateral surface area of composite figures, rectangular & triangular prisms
- Condensed: Determine total surface area & lateral surface area of composite figures, cylinders & cones
- Condensed: Determine total surface area & lateral surface area of composite figures, cylinders & hemispheres
- Condensed: Determine total surface area & lateral surface area of composite figures, prisms & pyramids
- Condensed: Determine total surface area & lateral surface area of composite 3D figures
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Composite Figure Volume
- Determine volume of composite rectangular prisms
- Determine volume of composite figures, rectangular & triangular prisms
- Determine volume of composite figures, cylinders & cones
- Determine volume of composite figures, cylinders & hemispheres
- Determine volume of composite figures, prisms & pyramids
- Condensed: Determine volume of composite 3D figures
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Mixed Figure Surface Area & Volume
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Mixed Figure Lateral Surface Area
- Determine lateral surface area of prisms
- Determine lateral surface area of prisms & cylinders
- Determine lateral surface area of composite figures, rectangular & triangular prisms, not requiring Pythagorean theorem
- Given net, determine lateral surface area of prisms & pyramids, real-world context
- Condensed: Determine lateral surface area of 3D figures
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Mixed Figure Surface Area
- Determine surface area of prisms & pyramids
- Determine surface area of prisms, pyramids, cones, cylinders, & spheres
- Determine surface areas of 3D figures, no circles
- Determine surface areas of 3D figures
- Determine surface area of 3D figure, including calculator π approximation
- Determine surface area of 3D figures, real-world context
- Determine surface area of composite figures, rectangular & triangular prisms, not requiring Pythagorean theorem
- Given surface area, determine dimension of 3D figure, no visual provided
- Determine lateral surface area of prisms & cylinders
- Determine lateral & total surface area of prisms & cylinders, including real-world context
- Given net, determine surface area of rectangular prism
- Given net, determine surface area of rectangular & triangular prisms & pyramids
- Given net, determine lateral surface area of prisms
- Given net, determine surface area of prisms & pyramids
- Condensed: Given net, determine surface area & lateral surface area of prisms & pyramids, including real-world context
- Condensed: Determine surface area of 3D figures
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Mixed Figure Volume
- Determine volumes of rectangular & triangular prisms, fractional dimensions
- Determine volume of cylinders, cones, & spheres
- Determine volume of cylinders, cones, & spheres, including real-world context
- Determine volumes of 3D figures
- Determine volume of 3D figures, real-world context
- Condensed: Determine volume of 3D figures
- Given volume, determine dimension of 3D figure, no visual provided
- Identify & determine relationship between volumes of rectangular prisms & pyramids
- Identify relationship between volume of cone & cylinder with same base & height
- Identify & determine relationship between volumes of triangular prisms & pyramids
- Condensed: Identify & determine relationship between volumes of prisms & pyramids
- Determine volume of composite rectangular prisms
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Mixed Figure Missing Dimension
- Condensed: Given surface area or volume, determine dimension of 3D figure
- Condensed: Given surface area or volume, determine dimension of 3D figure, no visual provided
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Similarity & Scale Factor
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Similar Figures
- Identify similar polygons
- Determine similarity of triangles using AA similarity
- Determine dimensions in similar figures
- Determine dimensions in similar figures, whole number dimensions
- Determine dimensions using similar figures & indirect measurements
- Given similar figures, identify proportion of side lengths, image orientations differ
- Given similar figures, identify proportion of side lengths, triangles & quadrilaterals
- Given similar figures, identify proportion of side lengths
- Given scale, determine specified dimension in scaled figure, real-world context
- Given two circles, determine scale factor or missing dimension
- Given two circles, determine scale factor of area or missing area
- Condensed: Determine or apply scale factor between circles
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Comparing Area, Perimeter, & Sides
- Determine scale factor or perimeter of dilated figures
- Determine scale factor or area of dilated figures
- Given similar rectangles, determine perimeter
- Given similar triangles, determine perimeter
- Given similar triangles, determine area
- Given similar cones, determine surface area
- Compare measurements of scaled shapes, including 3D shapes
- Compare measurements drawn with different scale factors
- Given scale factor or length of corresponding side, determine perimeter or area of similar triangle
- Given scale, determine area in scaled figure, real-world context
- Determine parts using similar triangles, including real-world context
- Determine edge, surface area, or volume of similar solids
- Given similar squares, determine area & side length
- Given similar squares, determine perimeter & side length
- Given similar rectangles, determine area
- Given similar cones, determine volume
- Given similar pyramids, determine surface area
- Given similar prisms, determine surface area
- Given similar spheres, determine volume
- Given similar pyramids, determine volume
- Given similar prisms, determine volume
- Given similar cylinders, determine volume
- Given similar cylinders, determine surface area
- Condensed: Given similar 2D figures, determine area or perimeter
- Given similar spheres, determine surface area
- Condensed: Given similar 3D figures, determine surface area or volume
- Identify scale factor of dilations, on coordinate plane
- Identify scale factor of dilations, not on coordinate plane
- Condensed: Identify scale factor of dilations
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Circles
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Parts of a Circle
- Identify components of circles
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Arcs, Segments, & Angles of Circles
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Angles in Circles
- Determine relationship between congruent arcs & congruent central angles
- Given tangent & other segments, determine angle
- Given central angle or arc measure, determine inscribed angle
- Given isosceles triangle in circle, determine angle measure at vertex of triangle
- Given inscribed isosceles triangle, determine base angle
- Given arc length & radius, determine central angle
- Given two secants intersecting inside circle, determine angle
- Given one chord & one secant of circle, determine angle
- Given two secants intersecting outside circle, determine angle
- Given two tangents to circle, determine angle
- Given secant & tangent to circle, determine angle
- Condensed: Given secants, tangents, & chords, determine angles
- Given chord, secant, & tangent on same circle, determine angles & arcs
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Arc Lengths of Circles
- Given arc measure & radius, determine arc length
- Apply arc addition postulate to determine arc measures
- Apply arc addition postulate to determine arc measures, including algebraic expressions
- Given inscribed isosceles triangle, determine measure of arc intercepted by base of triangle
- Determine relationship between congruent chords & congruent arcs
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Segments in Circles
- Given chord & radius, determine length
- Given two chords of circle, determine length
- Given two secants of circle, determine length, including algebraic expressions
- Given secant & tangent to circle, determine length
- Given secants, tangents, & chords, determine length
- Given tangent & other segments or circle inscribed in polygon, determine lengths
- Given tangents to circles, determine lengths, algebraic expressions
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Arcs, Segments, & Angles
- Given inscribed angle, determine central angle & arc measure
- Given isosceles triangle in circle, determine angle or arc measure
- Given inscribed right triangle, determine inscribed angle or arc measure
- Given inscribed angle formed by chord & tangent, determine angle or arc measure
- Given inscribed right triangle & tangent, determine angle or arc measure
- Given intersecting chords, determine angle or arc measure
- Given two diameters, radius, & two angles, determine angle or arc measure
- Condensed: Determine inscribed angles, central angles, & arc measures
- Condensed: Given inscribed right triangle, determine angle or arc measure
- Given inscribed isosceles triangle or isosceles triangle in circle, determine angle or arc measure
- Given tangent & secant intersecting at point of tangency, determine angles
- Determine relationship between congruent chords & congruent central angles
- Given arc length & central angle, determine circumference
- Condensed: Determine circumferences, arc lengths, & central angles
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Sector Area & Segment of Circles
- Determine area of sector
- Given radius & arc measure, determine area of circular segment
- Given chord length & arc measure, determine area of circular segment
- Given radius & arc measure of 60°, 90°, or 120°, determine area of circular segment
- Given chord length & arc measure of 60°, 90°, or 120°, determine area of circular segment
- Determine areas of circular segments
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Inscribed Figures
- Given circle inscribed in isosceles trapezoid, determine dimension or area
- Determine angles of quadrilateral inscribed in circle, including algebraic expressions
- Given inscribed isosceles triangle, determine base angle
- Given inscribed isosceles triangle, determine measure of arc intercepted by base of triangle
- Given inscribed right triangle, determine inscribed angle or arc measure
- Given inscribed right triangle & tangent, determine angle or arc measure
- Condensed: Given inscribed right triangle, determine angle or arc measure
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Equations of Circles
- Given center & radius, determine equation of circle
- Given equation of circle, identify center & radius
- Given graph, determine equation of circle
- Given equation of circle in standard form, identify graph
- Given equation of circle in general form, determine standard form
- Given equation of circle, determine area
- Condensed: Determine circle equations, centers, radii, & areas
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Geometric Modeling
- Apply concepts of density based on area & volume, real-world context
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Transformations
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Reflections
- Determine coordinates of reflected points
- Given coordinate vertices of figure, determine reflected image
- Given figure on coordinate plane, determine reflected coordinates
- Identify rule or reflected point on coordinate plane
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Rotations
- Given coordinate vertices of figure, determine rotated image
- Given figure on coordinate plane, determine rotated coordinates
- Identify rule or rotated point on coordinate plane
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Translations
- Given coordinate vertices of figure, determine translated image
- Given figure on coordinate plane, determine translated coordinates
- Identify rule or determine translated point on coordinate plane
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Dilations
- Identify characteristics of dilations
- Identify rule or dilated point on coordinate plane, including variable scale factors
- Given scale factor, determine dimension
- Given scale factor, determine coordinates of image, pre-image not centered at origin
- Condensed: Given scale factor, determine coordinates of image
- Given scale factor, determine coordinates of image, pre-image centered at origin
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Mixed Transformations
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Lines, Angles, & Segments Transformations
- Identify characteristics of transformed lines
- Identify characteristics of transformed line segments
- Identify characteristics of transformed angles
- Identify characteristics of transformed parallel lines
- Identify characteristics of transformed lines, segments, & angles
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Figure Transformations
- Given congruent figures, identify description of transformations
- Identify characteristics of transformations
- Given similar figures, identify description of transformations
- Identify reflections & rotations on coordinate plane
- Identify congruence transformations
- Composition of transformations on coordinate plane
- Identify rule for transformed shape on coordinate plane
- Identify rule or determine transformed point on coordinate plane
- Condensed: Given similar or congruent figures, identify description of transformations
- Condensed: Identify rule or determine transformed point on coordinate plane
- Condensed: Given figure on coordinate plane or coordinate vertices, determine transformed image or coordinates
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Probability
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Addition Rule
- Determine “or” probabilities, including “and” situations
- Determine “or” probabilities
- Determine “or” probabilities
- Determine “or” probabilities as fractions, decimals, or percents
- Determine “or” probabilities as fractions
- Given visual model, determine “or” probability as fraction, decimal, or percent
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Multiplication Rule
- Determine “and” probabilities, independent events, two distinct sample spaces
- Determine “and” probabilities, independent events, same sample space
- Determine “and” probabilities, independent events, visuals provided
- Determine “and” probabilities, independent & dependent events
- Determine “and” probabilities, independent & dependent events, including complementary events
- Determine “and” probabilities, dependent events
- Determine “and” probabilities, dependent events, multiple choice
- Given visual model, determine “and” probability as fraction, decimal, or percent, dependent events
- Determine probabilities of flipping coins specified number of times
- Determine probabilities of flipping coins & rolling die
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Conditional Probability
- Determine conditional probabilities from two-way frequency tables
- Determine conditional probabilities, including two-way frequency tables
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Parabolas
- Determine intervals where quadratic function is positive or negative
- Given graph or table of quadratic function, determine x- & y- intercepts
- Given focus & directrix of parabola, determine equation
- Given focus & directrix of parabola, determine equation in standard form