1. Lesson 6.5 Similarity and Measurement
Essential Question: How do you find unknown side lengths of similar figures?

2. Before we start…
A man who is 6 feet tall is standing near a saguaro cactus. The length of the man’s shadow is 2 feet. The cactus casts a shadow 5 feet long. How tall is the cactus?

3. What are similar figures?
Figures that have the same shape, but not the same size ~
You identify corresponding parts in similar figures

4. What are corresponding parts?
The sides or angles that have the same relative position in similar figures

6. How do you find unknown side lengths of similar figures?
Write a proportion setting corresponding sides lengths ratios equal to each other.

7. Given 𝐴𝐵𝐶𝐷~𝐸𝐹𝐺𝐻, find 𝐸𝐻.

8. Given ∆𝑆𝑇𝑈~∆𝐷𝐸𝐹, find 𝐷𝐹.

9. Given 𝐽𝐾𝐿𝑀~𝑃𝑄𝑅𝑆, find 𝑃𝑄.

10. A man who is 74 inches tall stands beside a palm tree
A man who is 74 inches tall stands beside a palm tree. The length of the man’s shadow is 26 inches. The palm tree’s shadow is 80 inches long. How tall is the palm tree?

11. The shadow cast by a 4-foot tall female ostrich is 10 feet long
The shadow cast by a 4-foot tall female ostrich is 10 feet long. A male ostrich standing nearby casts a shadow that is 15 feet long. How tall is the male ostrich?

12. At a certain time of day, a person who is 6 feet tall casts a 3-foot shadow. At the same time, a tree casts an 11-foot shadow. The triangles formed are similar. Find the height of the tree.

13. A farmer who is 72 inches tall is standing beside a silo that has a height of 140 feet. The length of the silo’s shadow is 31.5 feet. What is the length of the farmer’s shadow?

14. Given ∆𝐴𝐵𝐶~∆𝐷𝐸𝐶, find 𝐵𝐸.

15. Given ∆𝐴𝐵𝐶~∆𝐷𝐸𝐶, find 𝐵𝐸.

16. Given ∆𝑃𝑄𝑅~∆𝑆𝑇𝑅, find 𝑄𝑇.

17. How do you find unknown side lengths of similar figures?

18. Ticket Out the Door
Given 𝑃𝑄𝑅𝑆~𝑊𝑋𝑌𝑍, find 𝑌𝑍.