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Find the length of each segment. 1. 2.

WARM-UP. Find the length of each segment. 1. 2. SR = 25, ST = 15. Using Proportional Relationships 7-5. I can apply properties of similar figures. THE HOOVER DAM. What if there was internal seepage in the dam? .

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Find the length of each segment. 1. 2.

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  1. WARM-UP Find the length of each segment. 1.2. SR = 25, ST = 15

  2. Using Proportional Relationships7-5 • I can apply properties of similar figures.

  3. THE HOOVER DAM

  4. What if there was internal seepage in the dam? You would need to know the thickness of the dam at that location to design a fix. 3316 ft Lake Mead 3302 ft 7,264 ft ? Colorado River 660 ft

  5. Safe Stopping Distance Calculation for Road Design You can use Similarity Properties of a triangle to help in the design. Braking Time Perception/ Reaction Time

  6. Helpful Hint Whenever dimensions are given in both feet and inches, you must convert them to either feet or inches before doing any calculations. Indirect measurementis any method that uses formulas, similar figures, and/or proportions to measure an object. The following example shows one indirect measurement technique. ***Used extensively in land surveying**** Who/When else could use indirect measurements?

  7. Example Tyler wants to find the height of a telephone pole. He measured the pole’s shadow and his own shadow and then made a diagram. What is the height h of the pole? Step 1 Convert the measurements to inches. AB = 7 ft 8 in. = (7  12) in. + 8 in. = 92 in. BC = 5 ft 9 in. = (5  12) in. + 9 in. = 69 in. FG = 38 ft 4 in. = (38  12) in. + 4 in. = 460 in. Step 2 Find similar triangles. Because the sun’s rays are parallel, A  F. Therefore ∆ABC ~ ∆FGH by AA ~.

  8. Step 3 Find h. 92h = 69  460 h = 345 The height h of the pole is 345 inches, or 28 feet 9 inches.

  9. Your Turn A student who is 5 ft 6 in. tall measured shadows to find the height LM of a flagpole. What is LM? 60(h) = 66  170 h = 187 The height of the flagpole is 187 in., or 15 ft. 7 in.

  10. Similarity Ratio: Perimeter Ratio: P = P = Area Ratio: A = A =

  11. Example The similarity ratio of ∆LMN to ∆QRS is Perimeter Ratio = Area Ratio = Given that ∆LMN:∆QRT, find the perimeter P and area A of ∆QRS. Perimeter Area 13P = 36(9.1) 132A = (9.1)2(60) P = 25.2 A = 29.4 cm2

  12. Example ∆ABC ~ ∆DEF, BC = 4 mm, and EF = 12 mm. If P = 42 mm and A = 96 mm2 for ∆DEF, find the perimeter and area of ∆ABC. Perimeter Area 12P = 42(4) 122A = (4)2(96) P = 14 mm

  13. Your Turn ∆ABC ~ ∆DEF. Find the perimeter and area of ∆ABC. P = 27 in., A = 31.5 in2

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