1 / 11

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.

abbott
Download Presentation

EXAMPLE 1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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. = h59 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. 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. ANSWER 12 2. EGF ~ GHF~ EHG ; ANSWER 5 60 LMJ ~ MKJ~ LKM ; 13 for Examples 1 and 2 GUIDED PRACTICE Identify the similar triangles. Then find the value of x.

  6. Find the value of y. Write your answer in simplest radical form. Draw the three similar triangles. STEP 1 EXAMPLE 3 Use a geometric mean SOLUTION

  7. 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 Use a geometric mean Substitute. 27 = y2 Cross Products Property Take the positive square root of each side. Simplify.

  8. 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 Find a height using indirect measurement 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.

  9. 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 Find a height using indirect measurement SOLUTION By Theorem 7.6, you know that 8.5 is the geometric mean of w and 5. Write a proportion. Solve for w.

  10. 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. for Examples 3 and 4 GUIDED PRACTICE 3.In Example 3, which theorem did you use to solve fory? Explain.

  11. about 8.93 ft ANSWER for Examples 3 and 4 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?

More Related