Curriculum Framework

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

Circles

Constructing Congruent Segments and Angles

Constructing Parallel and Perpendicular Lines

G.CO.2: Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

Dilations

Reflections

Rotations, Reflections, and Translations

Translations

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

Dilations

Reflections

Rotations, Reflections, and Translations

Translations

G.CO.5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

Dilations

Reflections

Rotations, Reflections, and Translations

Translations

G.CO.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 decide if they are congruent.

Proving Triangles Congruent

Reflections

Rotations, Reflections, and Translations

Translations

G.CO.8: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

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

G.CO.10: Prove theorems about triangles.

Pythagorean Theorem

Triangle Angle Sum

Triangle Inequalities

G.CO.11: Prove theorems about parallelograms.

Parallelogram Conditions

Special Parallelograms

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

Constructing Congruent Segments and Angles

Constructing Parallel and Perpendicular Lines

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

G.SRT.1.b: The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

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

G.GPE.1: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

Circles

Distance Formula

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

G.GPE.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

Correlation last revised: 5/8/2018

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