1: Congruence

1: Experiment with transformations in the plane

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

2: Understand congruence in terms of rigid motions

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.

Proving Triangles Congruent

3: Prove geometric theorems

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

Investigating Angle Theorems

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

4: Make geometric constructions

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

2: Similarity, Right Triangles, and Trigonometry

5: Understand similarity in terms of similarity transformations

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.

Dilations
Similar Figures

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.

Similar Figures

3: Circles

6: Understand and apply theorems about circles

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

Inscribed Angles

4: Expressing Geometric Properties with Equations

7: Translate between the geometric description and the equation for a conic section

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

8: Use coordinates to prove simple geometric theorems algebraically

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

Distance Formula