2: Justify theorems related to pairs of angles, including angles formed by parallel and perpendicular lines, vertical angles, adjacent angles, complementary angles, and supplementary angles.

Investigating Angle Theorems - Activity A

3: Verify the relationships among different classes of polygons by using their properties.

3.1: Determining the missing lengths of sides or measures of angles in similar polygons

Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

4: Determine the measure of interior and exterior angles associated with polygons.

4.1: Verifying the formulas for the measures of interior and exterior angles of polygons inductively and deductively

Triangle Angle Sum - Activity A

5: Solve real-life and mathematical problems using properties and theorems related to circles, quadrilaterals, and other geometric shapes.

5.1: Determining the equation of a circle given its center and radius

Circles

6: Apply the Pythagorean Theorem to solve application problems, expressing answers in simplified radical form or as decimal approximations, using Pythagorean triples when applicable.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
Simplifying Radicals - Activity A

7: Use the ratios of the sides of special right triangles to find lengths of missing sides.

7.1: Deriving the ratios of the sides of 30-60-90 and 45-45-90 triangles

Perimeters and Areas of Similar Figures

8: Deduce relationships between two triangles, including proving congruence or similarity of the triangles from given information, using the relationships to solve problems and to establish other relationships.

8.1: Determining the geometric mean to find missing lengths in right triangles

Similarity in Right Triangles

10: Find the missing measures of sides and angles in right triangles by applying the right triangle definitions of sine, cosine, and tangent.

Classifying Triangles
Cosine Function
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Function
Tangent Ratio
Unit Circle

11: Determine the areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics.

Rectangle: Perimeter and Area

12: Apply distance, midpoint, and slope formulas to solve problems and to confirm properties of polygons.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
Slope - Activity B

13: Identify the coordinates of the vertices of the image of a given polygon that is translated, rotated, reflected, or dilated.

Dilations
Reflections
Rotations, Reflections and Translations
Translations

16: Calculate surface areas and volumes of solid figures, including spheres, cones, and pyramids.

16.1: Developing formulas for surface area and volume of spheres, cones, and pyramids

Pyramids and Cones - Activity A
Surface and Lateral Area of Pyramids and Cones

16.2: Calculating specific missing dimensions of solid figures from surface area or volume

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

16.3: Determining the relationship between the surface areas of similar figures and volumes of similar figures

Perimeters and Areas of Similar Figures

17: Analyze sets of data from geometric contexts to determine what, if any, relationships exist.

17.2: Calculating probabilities arising in geometric contexts

Geometric Probability - Activity A

18: Construct with precision a circle graph to represent data from given tables or classroom experiments.

Geometric Probability - Activity A
Probability Simulations