1. 7.3 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Use Similar Right Triangles

2. 7.3 Warm-Up ANSWER Yes; the AA Similarity Postulate 1. Are these triangles similar? If so, give the reason.

3. 7.3 Warm-Up ANSWER 50 2. Find x.

4. 7.3 Example 1 Identify the similar triangles in the diagram. SOLUTION Sketch the three similar right triangles so that the corresponding angles and sides have the same orientation. TSU ~ RTU ~ RST

5. 7.3 Example 2 Swimming Pool The diagram below shows a cross- section of a swimming pool. What is the maximum depth of the pool?

6. 7.3 Example 2 STEP 1 Identify the similar triangles and sketch them. RST ~ RTM ~ TSM SOLUTION

7. 7.3 Example 2 64 h = 165 152 Substitute. 165h = 64(152) Cross Products Property h 59 Solve for h. STEP 2 Find the value of h. Use the fact that RST ~ RTM to write a proportion. ST TM = SR TR Corresponding side lengths of similar triangles are in proportion.

8. 7.3 Example 2 STEP 3 Read the diagram. You can see that the maximum depth of the pool is h + 48, which is about 59 + 48 = 107 inches. The maximum depth of the pool is about 107 inches.

9. 7.3 Guided Practice Identify the similar triangles. Then find the value of x. 1. EGF ~ GHF ~ EHG ; 12 5 ANSWER 2. LMJ ~ MKJ ~ LKM ; 60 13 ANSWER

10. 7.3 Example 3 Find the value of y. Write your answer in simplest radical form. SOLUTION STEP 1 Draw the three similar triangles.

11. 7.3 Example 3 STEP 2 Write a proportion. length of hyp. of RQS length of hyp. of RPQ = length of shorter leg of RQS length of shorter leg of RPQ y 9 = 3 y 27 = y 2 27 = y 3 3 = y Simplify. Take the positive square root of each side. Substitute. Cross Products Property

12. 7.3 Example 4 Rock Climbing Wall To find the cost of installing a rock wall in your school gymnasium, you need to find the height of the gym wall. You use a cardboard square to line up the top and bottom of the gym wall. Your friend measures the vertical distance from the ground to your eye and the distance from you to the gym wall. Approximate the height of the gym wall.

13. 7.3 Example 4 SOLUTION By Theorem 7.6, you know that 8.5 is the geometric mean of w and 5. 8.5 w = 5 Write a proportion. w 14.5 Solve for w. So, the height of the wall is 5 + w 5 + 14.5 = 19.5 feet.

14. 7.3 Guided Practice 3. In Example 3, which theorem did you use to solve for y ? Explain. Theroem 7.7 ; This was used to set the ratios of the hypotenuse of the large triangle to the shorter leg and the hypotenuse of the small triangle to the shorter leg equal to each other. ANSWER

15. 7.3 Guided Practice 4. Mary is 5.5 feet tall. How far from the wall in Example 4 would she have to stand in order to measure its height? ANSWER about 8.93 ft

16. 7.3 Lesson Quiz 1. Identify the three similar right triangles in the diagram. ANSWER XYZ ~ XWY ~ YWZ

17. 7.3 Lesson Quiz Find the value of the variable. 2. ANSWER 3 5

18. 7.3 Lesson Quiz 215 ANSWER Find the value of the variable. 3.