Geometry Skills

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Foundations
- 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
- 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
- Spherical & Euclidean Geometry
  - Identify properties of spherical geometry
  - Identify properties of Euclidean & spherical geometry
  - Identify triangle angle sums in Euclidean & spherical geometry
Distance, Midpoint, & Segment Addition Postulate
- 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
- 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
- Distance & Midpoint
  - Given midpoint or distance between points, determine missing endpoint
  - Condensed: Determine distance or midpoint on number line
- 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
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
Angles
- Classifying Angles
  - Classify angles from figure
  - Identify angle names
  - Identify angle pairs
  - Identify types of angles in figures
- 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
- 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
- Angle Pairs
  - 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
  - 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
  - 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
  - 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
  - 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
  - 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
  - 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
  - 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
Parallel & Perpendicular Lines
- Equations of Parallel & Perpendicular Lines
  - 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
  - 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
  - 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
  - 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
- 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
Congruence
- Determine missing steps in proofs involving angles
- Determine missing steps in proofs involving segments
- Determine missing steps in proofs involving parallel lines
Triangles
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Medians & Centroids
  - Given median of triangle, determine variable or length of bisected side, algebraic expressions
  - Apply centroid theorem
  - Determine coordinates of centroid of triangles
- 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
Triangle Similarity & Congruence
- 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
- 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
Right Triangles & Trigonometry
- 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
- 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
- Special Right Triangles
  - 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
  - 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
  - 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
  - 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
- 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
Quadrilateral Properties
- Rectangle Properties
  - Determine angle measures in rectangles with diagonals
  - Given diagonals with algebraic expressions in rectangle, determine variable or diagonal length
- 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
- 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
- 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
- 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
- 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
Polygons
- 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
- Polygon Congruence
  - Identify corresponding parts from congruence statement or determine congruence statement from figures
Classifying 2D & 3D Figures
- 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
- 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
Perimeter & Area
- Rectangle Perimeter & Area
  - Rectangle Perimeter
    - 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
    - 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
    - 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
  - Rectangle Area
    - 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
    - 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
    - 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
  - 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
- 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
- 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
- Trapezoid Area
  - Determine area of trapezoids using models that decompose & rearrange parts
  - Determine area of trapezoids
  - Given area & base lengths of trapezoid, determine height
- Circle Area & Circumference
  - 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
  - Circle Area
    - Given radius or diameter, determine area
    - Determine area of circle, exact answers, including real-world context
    - Determine areas of semicircles & quarter circles
  - 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
- Polygon Perimeter & Area
  - Polygon Perimeter
    - Determine perimeter of polygons, including real-world context
    - Given coordinates of vertices, determine side lengths & perimeter of polygons
  - 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
- Mixed Figure Perimeter & Area
  - 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
  - Mixed Figure Formulas & Applications
    - Identify formulas for area & perimeter of basic shapes
    - Determine dimensions that maximize area of rectangle for given perimeter
- 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
- 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
Surface Area & Volume
- 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
- 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
- Rectangular Prism Surface Area & Volume
  - 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
  - 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
  - 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
- Triangular Prism Surface Area
  - Determine surface area of triangular prisms
- 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
- 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
- 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
- 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
- Composite Figure Surface Area & Volulme
  - 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
  - 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
- Mixed Figure Surface Area & Volume
  - 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
  - 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
  - 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
  - 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
Similarity & Scale Factor
- 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
- 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
Circles
- Parts of a Circle
  - Identify components of circles
- Arcs, Segments, & Angles of Circles
  - 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
  - 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
  - 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
  - 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
- 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
- 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
- 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
Geometric Modeling
- Apply concepts of density based on area & volume, real-world context
Transformations
- 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
- 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
- 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
- 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
- Mixed Transformations
  - 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
  - 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
Probability
- 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
- 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
- Conditional Probability
  - Determine conditional probabilities from two-way frequency tables
  - Determine conditional probabilities, including two-way frequency tables
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