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EXAMPLE 1

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

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EXAMPLE 1

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

  2. 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

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

  4. = h 59 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. STEP 2 Find the value of h. Use the fact that RST ~ RTMto write a proportion. h TR 152 TM = SR ST 165 64 EXAMPLE 2 Find the length of the altitude to the hypotenuse Corresponding side lengths of similar triangles are in proportion. Substitute. 165h = 64(152) Cross Products Property Solve for h. The maximum depth of the pool is about 107 inches.

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

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

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

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

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

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