1. EXAMPLE 1 Identify similar triangles 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

2. EXAMPLE 2 Find the length of the altitude to the hypotenuse Swimming Pool The diagram below shows a cross-section of a swimming pool. What is the maximum depth of the pool?

3. EXAMPLE 2 Find the length of the altitude to the hypotenuse STEP 1 Identify the similar triangles and sketch them. RST ~ RTM ~ TSM SOLUTION

4. EXAMPLE 2 Find the length of the altitude to the hypotenuse 64 h = 165 152 Substitute. 165h = 64(152) Cross Products Property h 59 Solve for h. STEP 3 Read the diagram above. 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. 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.

5. GUIDED PRACTICE for Examples 1 and 2 Identify the similar triangles. Then find the value of x. 1.

6. GUIDED PRACTICE for Examples 1 and 2 GH GF = EG EF Corresponding side length of similar triangle are in proportion x 4 = 3 5 Substitute 5x = 12 Cross products property x 12 5 = Solve for x STEP 1The similar triangle are EGF ~ GHF STEP 2 To find the value of x Use the fact that EGF ~ EHG to write a population 1.

7. GUIDED PRACTICE for Examples 1 and 2 Identify the similar triangles. Then find the value of x. 2.

8. GUIDED PRACTICE for Examples 1 and 2 2. The similar triangle are LMJ ~ MKJ ~ LKM STEP 1 13 5 12 K L M J x STEP 2 To find the value of x. use the fact that LMJ ~ MKJ to write a peroration

9. GUIDED PRACTICE for Examples 1 and 2 KM JM = ML JL Corresponding side length of similar triangle are in proportion x 12 = 5 13 Substitute 13x = (12) (5) Cross products property x 60 13 = Solve for x 13x = 60