Unit 3: Similarity

Students extend rigid transformations to include dilations and define similar figures. They prove the Angle-Angle Triangle Similarity Theorem, use similar right triangles to prove the Pythagorean Theorem and its converse, and use similarity to solve problems.

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What this unit covers

A Properties of Dilations · 5 lessons

Goals

• Comprehend that dilations take angles to congruent angles and lines not passing through the center of the dilation to parallel lines.
• Create and interpret scaled drawings of figures.

Lessons

1. Scale Drawings
2. Scale of the Solar System (Optional)
3. Measuring Dilations
4. Dilating Lines and Angles
5. Splitting Triangle Sides with Dilation (Part 1)

B Similarity Transformations and Proportional Reasoning · 7 lessons

Goals

• Generate similarity statements about similar figures, and identify equivalent proportional relationships among side lengths.
• Use the Angle-Angle Triangle Similarity Theorem and the Triangle Angle Sum Theorem to show that two triangles are similar.

Lessons

1. Connecting Similarity and Transformations
2. Reasoning about Similarity with Transformations
3. Are They All Similar?
4. Conditions for Triangle Similarity
5. Other Conditions for Triangle Similarity (Optional)
6. Splitting Triangle Sides with Dilation (Part 2)
7. Practice with Proportional Relationships (Optional)

C Similarity in Right Triangles · 4 lessons

Goals

• Use similarity, proportionality, and the Pythagorean Theorem to solve problems involving right triangles.

Lessons

1. Using the Pythagorean Theorem and Similarity
2. Proving the Pythagorean Theorem
3. Converse of the Pythagorean Theorem
4. Finding All the Unknown Values in Triangles

D Let’s Put It to Work · 1 lesson

Lessons

1. Reflection Similarity