Geometry 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, realworld 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 “sameside interior” terminology
 Given parallel lines with transversal & angles, identify specified angle pairs, uses “sameside interior” terminology
 Given parallel lines with transversal & angle, determine & justify specified angle
 Given three parallel lines with two transversals, determine lengths
 Given nonparallel 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 & SameSide Interior Angles
 Given parallel lines with transversal & angle, determine corresponding angle
 Given parallel lines with transversal & angle, determine sameside interior angle
 Given parallel lines with transversal & angle, determine corresponding angle, algebraic expressions
 Given parallel lines with transversal & angle, determine sameside 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 xaxis
 Determine equation of line through specified point parallel or perpendicular to yaxis
 Condensed: Determine equation of line through specified point parallel or perpendicular to x or yaxis

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 SlopeIntercept Form or Standard Form
 Given two slopeintercept 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 slopeintercept form, determine equation of parallel line through specified point
 Given equation in slopeintercept form, determine equation of perpendicular line through specified point
 Given equation in slopeintercept 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, realworld context
 Identify parallel & perpendicular lines in figures, realworld context
 Identify parallel & perpendicular lines in figures
 Condensed: Identify types of lines in figures, realworld 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

AngleSide 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, realworld context
 Given two sides, determine missing side of right triangle, realworld context
 Solve problems using Pythagorean theorem, realworld context
 Given ratio of sides & one dimension, apply Pythagorean theorem to determine specified dimension, realworld context
 Determine side of right triangle or apply converse of Pythagorean theorem, including realworld 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

306090 Triangles
 Given 306090 triangle, determine side
 Given 306090 triangle & short leg, determine hypotenuse
 Given 306090 triangle & long leg, determine short leg
 Given 306090 triangle & short leg, determine long leg
 Given 306090 triangle & long leg, determine hypotenuse
 Given 306090 triangle & hypotenuse, determine short leg
 Given 306090 triangle & hypotenuse, determine long leg

454590 Triangles
 Given 454590 triangle, determine hypotenuse
 Given 454590 triangle, determine leg
 Given 454590 triangle, determine side

Application of Special Right Triangles
 Condensed: Given special right triangle, determine side
 Determine angles using special right triangle relationships, realworld context
 Determine sides using special right triangle relationships, realworld context
 Condensed: Determine angles or sides using special right triangle relationships, realworld 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, realworld context
 Determine sides & angles of triangles using law of cosines, realworld context
 Condensed: Determine sides & angles of triangles using law of sines or law of cosines, realworld 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 realworld context
 Condensed: Determine perimeter of rectangles, including realworld context

Application of Rectangle & Square Permimeter
 Given sides of rectangle, determine perimeter
 Determine perimeter of rectangles, realworld context
 Determine perimeter of rectangles, including decimal dimensions, realworld 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 realworld context

Application of Rectangle & Square Area
 Determine area of missing dimension of rectangles, realworld context
 Determine equations that represent area of rectangles, realworld context
 Given sides of rectangle & cost per square unit, determine area & total cost, realworld 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 realworld 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 realworld 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, realworld 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, realworld 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 realworld 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 realworld 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 realworld 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, realworld 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, realworld 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 realworld 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, realworld 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, realworld 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, realworld context
 Condensed: Given net, determine surface area & lateral surface area of prisms & pyramids, including realworld 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, realworld context
 Determine volume of cubes, whole numbers, decimals, or fractions, realworld 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 realworld 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, realworld 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 realworld context

Application of Rectangular Prism Volume
 Determine equations for volume of rectangular prisms, rational dimensions, realworld context
 Determine volume of rectangular prisms using various representations of cubic units, realworld context
 Determine volumes of rectangular prisms, rational dimensions, realworld context
 Determine volume of rectangular prisms & apply associative property to volume expressions
 Determine volume or edge of rectangular prisms, whole numbers or decimals, realworld context
 Determine volume of rectangular prisms, whole numbers, including realworld context
 Determine volume or edge of rectangular prisms, whole numbers, decimals, or fractions, realworld context
 Condensed: Determine volumes or edges of rectangular prisms, whole numbers, decimals, or fractions, including realworld 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, realworld 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, realworld 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 realworld 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 realworld 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 realworld context
 Determine volumes of 3D figures
 Determine volume of 3D figures, realworld 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, realworld 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, realworld context
 Determine parts using similar triangles, including realworld 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, realworld 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, preimage not centered at origin
 Condensed: Given scale factor, determine coordinates of image
 Given scale factor, determine coordinates of image, preimage 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 twoway frequency tables
 Determine conditional probabilities, including twoway 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