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
    • 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