7.3 use similar right triangles
- 1. 7.3 Use Similar Right Triangles 7.3 Bell Thinger 1. Are these triangles similar? If so, give the reason. ANSWER 2. Find x. Yes; the AA Similarity Postulate ANSWER 50
- 2. 7.3
- 3. Example 1 7.3 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
- 4. Example 2 7.3 Swimming Pool The diagram below shows a crosssection of a swimming pool. What is the maximum depth of the pool?
- 5. Example 2 7.3 SOLUTION STEP 1 Identify the similar triangles and sketch them. RST ~ RTM ~ TSM STEP 2 Find the value of h. Use the fact that RST ~ RTM to write a proportion. Corresponding side lengths of TM TR = similar triangles are in proportion. ST SR h 152 = Substitute. 64 165 165h = 64(152) h ≈ 59 Cross Products Property Solve for h.
- 6. Example 2 7.3 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. The maximum depth of the pool is about 107 inches.
- 7. Guided Practice 7.3 Identify the similar triangles. Then find the value of x. 1. ANSWER EGF ~ GHF ~ LMJ ~ MKJ ~ EHG ; 12 5 2. ANSWER LKM ; 60 13
- 8. Example 3 7.3 Find the value of y. Write your answer in simplest radical form. SOLUTION STEP 1 Draw the three similar triangles.
- 9. Example 3 7.3 STEP 2 Write a proportion. length of hyp. of length of hyp. of RPQ length of shorter leg of = RQS length of shorter leg of 9 y y = 3 RPQ RQS Substitute. 27 = y2 Cross Products Property 27 = y Take the positive square root of each side. 3 3=y Simplify.
- 10. 7.3
- 11. Example 4 7.3 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. 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.
- 12. Example 4 7.3 SOLUTION By Theorem 7.6, you know that 8.5 is the geometric mean of w and 5. w 8.5 8.5 = 5 w ≈ 14.5 Write a proportion. Solve for w. So, the height of the wall is 5 + w ≈ 5 + 14.5 = 19.5 feet.
- 13. Guided Practice 7.3 3. 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? ANSWER about 8.93 ft
- 14. Exit Slip 7.3 1. Identify the three similar right triangles in the diagram. ANSWER XYZ ~ XWY ~ YWZ
- 15. Exit Slip 7.3 Find the value of the variable. 2. ANSWER 3 5
- 16. Exit Slip 7.3 Find the value of the variable. 3. ANSWER 2 15
- 17. 7.3 Homework Pg 471-474 #6, 14, 18, 23, 30