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Warm Up

Use Similar Right Triangles. Warm Up. Lesson Presentation. Lesson Quiz. 1. Are these triangles similar? If so, give the reason. Yes; the AA Similarity Postulate. ANSWER. Warm-Up. 2. Find x. 50. ANSWER. Warm-Up. TSU ~ RTU ~ RST. Example 1.

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Warm Up

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  1. Use Similar Right Triangles Warm Up Lesson Presentation Lesson Quiz

  2. 1.Are these triangles similar? If so, give the reason. Yes; the AA Similarity Postulate ANSWER Warm-Up

  3. 2.Findx. 50 ANSWER Warm-Up

  4. TSU ~ RTU ~ RST Example 1 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.

  5. Swimming Pool The diagram below shows a cross-section of a swimming pool. What is the maximum depth of the pool? Example 2

  6. STEP 1 Identify the similar triangles and sketch them. RST ~ RTM ~ TSM Example 2 SOLUTION

  7. = h59 STEP 2 Find the value of h. Use the fact that RST ~ RTMto write a proportion. h 152 TM TR = ST SR 64 165 Example 2 Corresponding side lengths of similar triangles are in proportion. Substitute. 165h = 64(152) Cross Products Property Solve for h.

  8. STEP 3 Read the diagram. You can see that the maximum depth of the pool is h + 48, which is about 59 + 48 = 107 inches. Example 2 The maximum depth of the pool is about 107 inches.

  9. 1. ANSWER 12 2. EGF ~ GHF ~ EHG ; 5 60 LMJ ~ MKJ ~ LKM ; 13 ANSWER Guided Practice Identify the similar triangles. Then find the value of x.

  10. Find the value of y. Write your answer in simplest radical form. Draw the three similar triangles. STEP 1 Example 3 SOLUTION

  11. Write a proportion. STEP 2 length of shorter leg of RPQ length of hyp. of RPQ = length of hyp. of RQS length of shorter leg of RQS y 9 = y 3 27 = y 3 3 = y Example 3 Substitute. 27 = y2 Cross Products Property Take the positive square root of each side. Simplify.

  12. Rock Climbing Wall To find the cost of installing a rock wall in your school gymnasium, you need to find the height of the gym wall. Example 4 You use a cardboard square to line up the top and bottom of the gym wall. Your friend measures the vertical distance from the ground to your eye and the distance from you to the gym wall. Approximate the height of the gym wall.

  13. 8.5 w = 5 8.5 w 14.5 So, the height of the wall is 5 + w 5 + 14.5 = 19.5 feet. Example 4 SOLUTION By Theorem 7.6, you know that 8.5 is the geometric mean of w and 5. Write a proportion. Solve for w.

  14. ANSWER Theroem 7.7; This was used to set the ratios of the hypotenuse of the large triangle to the shorter leg and the hypotenuse of the small triangle to the shorter leg equal to each other. Guided Practice 3.In Example 3, which theorem did you use to solve fory? Explain.

  15. about8.93 ft ANSWER Guided Practice 4. Mary is 5.5 feet tall. How far from the wall in Example 4 would she have to stand in order to measure its height?

  16. 1. Identify the three similar right triangles in the diagram. XYZ ~ XWY ~ YWZ ANSWER Lesson Quiz

  17. 2. 5 3 ANSWER Lesson Quiz Find the value of the variable.

  18. 3. 2 ANSWER 15 Lesson Quiz Find the value of the variable.

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