Geometry (Arizona Mathematics Standards)

Number and Quantity

• G.N-Q.A.1 Use units to understand and guide multistep problems, read units in formulas and choose scales and origins for graphs and data displays.
• G.N-Q.A.2 Define suitable quantities when building a descriptive model.
• G.N-Q.A.3 Report quantities with a level of accuracy that fits the limits of measurement.

Congruence (G-CO)

• G.G-CO.A.1 Know precise definitions of angle, circle, perpendicular and parallel lines and segment from undefined terms.
• G.G-CO.A.2 Represent transformations as functions on points and compare rigid motions with others such as stretches.
• G.G-CO.A.3 Describe the rotations and reflections that map a rectangle, parallelogram, trapezoid or regular polygon onto itself.
• G.G-CO.A.4 Define rotations, reflections and translations using angles, circles, perpendicular and parallel lines and segments.
• G.G-CO.A.5 Draw the image of a figure under a rotation, reflection or translation and specify sequences of moves.
• G.G-CO.B.6 Use rigid motions to transform figures, predict effects and decide whether two figures are congruent.
• G.G-CO.B.7 Use rigid motions to show triangles are congruent exactly when corresponding sides and angles are congruent.
• G.G-CO.B.8 Explain how the ASA, AAS, SAS and SSS congruence tests follow from defining congruence with rigid motions.
• G.G-CO.C.9 Prove theorems about lines and angles (vertical angles, angles with parallel lines, perpendicular bisector points).
• G.G-CO.C.10 Prove theorems about triangles (angle sum, isosceles base angles, midsegment, medians meeting at a point).
• G.G-CO.C.11 Prove theorems about parallelograms (opposite sides and angles, bisecting diagonals, rectangles' diagonals).
• G.G-CO.D.12 Make formal constructions with compass and straightedge, paper folding or software (copying, bisecting, perpendiculars, parallels).
• G.G-CO.D.13 Construct an equilateral triangle, square and regular hexagon inscribed in a circle.

Similarity, Right Triangles, and Trigonometry (G-SRT)

• G.G-SRT.A.1 Check by experiment how a dilation with a center and scale factor maps lines and scales segment lengths. (being checked)
• G.G-SRT.A.2 Use similarity transformations to decide if figures are similar and explain similarity of triangles through matching angles and proportional sides.
• G.G-SRT.A.3 Use similarity transformations to justify the AA, SAS and SSS tests for similar triangles.
• G.G-SRT.B.4 Prove triangle theorems such as the side-splitter theorem and the Pythagorean Theorem using similarity.
• G.G-SRT.B.5 Use congruence and similarity criteria to solve problems and prove relationships in figures.
• G.G-SRT.C.6 Understand that side ratios in right triangles depend on the angles, leading to the trigonometric ratios.
• G.G-SRT.C.7 Explain and use how sine and cosine of complementary angles are related.
• G.G-SRT.C.8 Use trig ratios, their inverses and the Pythagorean Theorem to find unknown measures in right triangles in context.

Circles (G-C)

• G.G-C.A.1 Prove that all circles are similar.
• G.G-C.A.2 Describe relationships among inscribed, central and circumscribed angles, radii and chords, including tangent and radius.
• G.G-C.A.3 Construct a triangle's inscribed and circumscribed circles and prove angle facts for cyclic quadrilaterals.
• G.G-C.B.5 Use similarity to show arc length is proportional to radius, define radians, derive sector area and convert degrees to radians.

Expressing Geometric Properties with Equations (G-GPE)

• G.G-GPE.A.1 Derive the equation of a circle from the Pythagorean Theorem and complete the square to find center and radius.
• G.G-GPE.B.4 Prove simple geometry theorems algebraically with coordinates.
• G.G-GPE.B.5 Prove the slope tests for parallel and perpendicular lines and apply them to problems.
• G.G-GPE.B.6 Find the point that divides a directed segment in a given ratio.
• G.G-GPE.B.7 Use coordinates (e.g. the distance formula) to find polygon perimeters and triangle and rectangle areas.

Geometric Measurement and Dimension (G-GMD)

• G.G-GMD.A.1 Give and check informal arguments for the volume formulas of cylinders, pyramids and cones.
• G.G-GMD.A.3 Solve problems using the formulas for the volume of a cylinder, pyramid, cone or sphere.
• G.G-GMD.B.4 Identify 2-D cross-sections of 3-D objects and 3-D objects formed by rotating 2-D shapes.

Modeling with Geometry (G-MG)

• G.G-MG.A.1 Use shapes and their measures to describe real objects (e.g. a tree trunk as a cylinder).
• G.G-MG.A.2 Use density by area or volume in modeling (e.g. people per square mile).
• G.G-MG.A.3 Use geometric methods to solve design problems with physical limits or cost goals.