### 1: Congruence

#### 1: Prove geometric theorems

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

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.).

### 2: Similarity, Right Triangles, and Trigonometry

#### 3: Prove theorems involving similarity

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

#### 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.

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

### 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.

### 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.

### 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.

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

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.