### G: Geometry

#### G.CO: Congruence

G.CO.A: Experiment with transformations in the plane.

G.CO.A.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, plane, distance along a line, and distance around a circular arc.

G.CO.A.2: Represent transformations in the plane in multiple ways, including technology. Describe transformations as functions that take points in the plane (pre-image) as inputs and give other points (image) as outputs. Compare transformations that preserve distance and angle measure to those that do not (e.g., translation versus horizontal stretch).

G.CO.A.3: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry the shape onto itself.

G.CO.A.4: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

G.CO.A.5: Given a geometric figure and a rigid motion, draw the image of the figure in multiple ways, including technology. Specify a sequence of rigid motions that will carry a given figure onto another.

G.CO.B: Understand congruence in terms of rigid motions.

G.CO.B.6: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to determine informally if they are congruent.

G.CO.C: Prove geometric theorems.

G.CO.C.9: Prove theorems about lines and angles.

G.CO.D: Make geometric constructions.

G.CO.D.12: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).

#### G.SRT: Similarity, Right Triangles, and Trigonometry

G.SRT.A: Understand similarity in terms of similarity transformations.

G.SRT.A.1: Verify informally the properties of dilations given by a center and a scale factor.

G.SRT.A.2: Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

G.SRT.A.3: Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

G.SRT.B: Prove theorems involving similarity.

G.SRT.B.4: Prove theorems about similar triangles.

G.SRT.B.5: Use congruence and similarity criteria for triangles to solve problems and to justify relationships in geometric figures.

G.SRT.C: Define trigonometric ratios and solve problems involving triangles.

G.SRT.C.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

G.SRT.C.8: Solve triangles.

G.SRT.C.8.a: Know and use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

#### G.C: Circles

G.C.A: Understand and apply theorems about circles.

G.C.A.2: Identify and describe relationships among inscribed angles, radii, and chords.

G.C.A.3: Construct the incenter and circumcenter of a triangle and use their properties to solve problems in context.

#### G.GPE: Expressing Geometric Properties with Equations

G.GPE.A: Translate between the geometric description and the equation for a circle.

G.GPE.A.1: Know and write the equation of a circle of given center and radius using the Pythagorean Theorem.

#### G.GMD: Geometric Measurement and Dimension

G.GMD.A: Explain volume and surface area formulas and use them to solve problems.

G.GMD.A.1: Give an informal argument for the formulas for the circumference of a circle and the volume and surface area of a cylinder, cone, prism, and pyramid.

G.GMD.A.2: Know and use volume and surface area formulas for cylinders, cones, prisms, pyramids, and spheres to solve problems.

Correlation last revised: 11/21/2018

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.