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
SOLUTION
STEP 1
Identify the similar triangles and sketch them.
RST ~ RTM ~ TSM

4. Find the length of the altitude to the hypotenuse
EXAMPLE 2
Find the length of the altitude to the hypotenuse
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. 64 h =
165
152
Substitute.
165h = 64(152)
Cross Products Property h
Solve for h.
STEP 3
Read the diagram. You can see that the maximum depth of the pool is h + 48, which is about = 107 inches.
The maximum depth of the pool is about 107 inches.

5. GUIDED PRACTICE
for Examples 1 and 2
Identify the similar triangles. Then find the value of x. 1.
EGF ~ GHF ~ EHG ; 12 5
ANSWER 2.
LMJ ~ MKJ ~ LKM ; 60 13
ANSWER