Download - EXAMPLE 1
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