1. Similarity in Right Triangles Geometry Unit 11, Day 7 Ms. Reed

2. Similarity in Right Triangles Right Triangles have specific relationships with the lengths of the legs, the hypotenuse and the altitude.

3. In groups of 2: We will be discovering ways to prove triangles similar. You will need: ruler long straight edge (ex. Planner) paper scissors

4. Step 1: Draw one diagonal on the piece of paper This should form 2 congruent triangles If congruent, cut the paper along the line of the diagonal.

5. Step 2: Fold the triangle to find the altitude so that the altitude intersects the hypotenuse. Once done correctly, cut along the altitude to create 2 more triangles.

6. Step 3: Label the bigger triangle as so: Label the other 2 triangles as so: 2 1 3 Shorter side longer side 4 5 6 7 8 9

7. Step 4: Compare the angles of all three triangles by placing them on top of each other. Which  s and  to  1? Which  s and  to  2? Which  s and  to  3? What is true about all 3 triangles?

8. Step 5: Find the similarity ratio between the Smallest triangle to the middle triangle Middle triangle to the largest triangle Smallest triangle to largest triangle

9. What we discovered! The altitude to the hypotenuse of a right triangle divides the triangle into 2 triangles, making all 3 triangles similar.

10. Name the corresponding sides for the following picture: Original: AB middle:___ small: ___ Original: BC middle:___ small: ___ Original: AC middle:___ small: ___ DB AD DC BD BC AB

11. Write a Similarity Statement for the following picture:  ABC ~  ______ ~  ______  ABC ~  BDC ~  ADB