EXAMPLE 1 Identify similar triangles

Identify the similar triangles in the diagram.

SOLUTIONSketch the three similar right triangles so that the corresponding angles and sides have the same orientation.

TSU ~ RTU ~ RST

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?

EXAMPLE 2 Find the length of the altitude to the hypotenuse

STEP 1Identify the similar triangles and sketch them.

RST ~ RTM ~ TSM

SOLUTION

EXAMPLE 2 Find the length of the altitude to the hypotenuse

64 h

=165152

Substitute.

165h = 64(152) Cross Products Property

h 59 Solve for h.

STEP 3Read 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 2Find the value of h. Use the fact that RST ~ RTM to write a proportion.

STTM

=SRTR Corresponding side lengths of

similar triangles are in proportion.

GUIDED PRACTICE for Examples 1 and 2

Identify the similar triangles. Then find the value of x.

1.

GUIDED PRACTICE for Examples 1 and 2

GHGF

=EGEF

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 1 The similar triangle are EGF ~ GHF

STEP 2 To find the value of x

Use the fact that EGF ~ EHG to write a population

1.

GUIDED PRACTICE for Examples 1 and 2

Identify the similar triangles. Then find the value of x.

2.

GUIDED PRACTICE for Examples 1 and 2

2. The similar triangle are LMJ ~ MKJ ~ LKM

STEP 1

13

5

12

KL

MJ

x

STEP 2 To find the value of x. use the fact that LMJ ~ MKJ to write a peroration

GUIDED PRACTICE for Examples 1 and 2

KMJM

=MLJL

Corresponding side length of similar triangle are in proportion

x12

= 5 13

Substitute

13x = (12) (5) Cross products property

x 6013

= Solve for x

13x = 60