### 1: Congruence

#### 1: 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

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

#### 3: Prove theorems involving similarity

G.SRT.4: Prove theorems about triangles.

Pythagorean Theorem

Similar Figures

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

Dilations

Perimeters and Areas of Similar Figures

Similarity in Right Triangles

#### 4: Define trigonometric ratios and solve problems involving right triangles

G.SRT.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.

Sine, Cosine, and Tangent Ratios

G.SRT.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Distance Formula

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

Sine, Cosine, and Tangent Ratios

### 3: Circles

#### 6: Find arc lengths and areas of sectors of circles

G.C.5: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

Chords and Arcs

### 4: Expressing Geometric Properties with Equations

#### 7: 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

### 5: Geometric Measurement and Dimension

#### 8: Explain volume formulas and use them to solve problems

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

Circumference and Area of Circles

Prisms and Cylinders

Pyramids and Cones

G.GMD.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

Prisms and Cylinders

Pyramids and Cones

Correlation last revised: 5/8/2018