## Geometry Skills

VIEW ALL SKILLS

• 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
• 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
• 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
• 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
• 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
• 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
• 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