Lesson 3 Menu 1.The quadrilaterals are similar. Write a similarity statement and find the scale factor of the larger quadrilateral to the smaller quadrilateral.

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Presentation transcript:

Lesson 3 Menu 1.The quadrilaterals are similar. Write a similarity statement and find the scale factor of the larger quadrilateral to the smaller quadrilateral. 2.The triangles shown in the figure are similar. Find x and y.

Lesson 3 MI/Vocab Identify similar triangles. Use similar triangles to solve problems.

Lesson 3 PS1

Lesson 3 TH1

Lesson 3 Ex1 In the figure,, and  ABC and  DCB are right angles. Determine which triangles in the figure are similar. Are Triangles Similar?

Lesson 3 Ex1 Answer: Therefore, by the AA Similarity Theorem, ΔABE ~ ΔCDE. Vertical angles are congruent, by the Alternate Interior Angles Theorem. Are Triangles Similar?

A.A B.B C.C D.D Lesson 3 CYP1 A.ΔOBW ~ ΔITW B.ΔOBW ~ ΔWIT C.ΔBOW ~ ΔTIW D.ΔBOW ~ ΔITW In the figure, OW = 7, BW = 9, WT = 17.5, and WI = Determine which triangles in the figure are similar.

Lesson 3 TH2

Lesson 3 Ex2 Parts of Similar Triangles ALGEBRA Given, RS = 4, RQ = x + 3, QT = 2x + 10, UT = 10, find RQ and QT.

Lesson 3 Ex2 Parts of Similar Triangles Since because they are alternate interior angles. By AA Similarity, ΔRSQ ~ ΔTUQ. Using the definition of similar polygons, Substitution Cross products

Lesson 3 Ex2 Parts of Similar Triangles Answer: RQ = 8; QT = 20 Distributive Property Subtract 8x and 30 from each side. Divide each side by 2. Now find RQ and QT.

Lesson 3 CYP2 1.A 2.B 3.C 4.D A.2 B.4 C.12 D.14 A. ALGEBRA Given AB = 38.5, DE = 11, AC = 3x + 8, and CE = x + 2, find AC.

Lesson 3 Ex3 INDIRECT MEASUREMENT Josh wanted to measure the height of the Sears Tower in Chicago. He used a 12-foot light pole and measured its shadow at 1 P.M. The length of the shadow was 2 feet. Then he measured the length of the Sears Tower’s shadow and it was 242 feet at that time. What is the height of the Sears Tower? Indirect Measurement

Lesson 3 Ex3 Since the sun’s rays form similar triangles, the following proportion can be written. Now substitute the known values and let x be the height of the Sears Tower. Substitution Cross products Indirect Measurement

Lesson 3 Ex3 Answer: The Sears Tower is 1452 feet tall. Simplify. Divide each side by 2. Indirect Measurement

1.A 2.B 3.C 4.D Lesson 3 CYP3 A.196 ftB. 39 ft C.441 ftD. 89 ft INDIRECT MEASUREMENT On her trip along the East coast, Jennie stops to look at the tallest lighthouse in the U.S. located at Cape Hatteras, North Carolina. At that particular time of day, Jennie measures her shadow to be 1 feet 6 inches in length and the length of the shadow of the lighthouse to be 53 feet 6 inches. Jennie knows that her height is 5 feet 6 inches. What is the height of the Cape Hatteras lighthouse to the nearest foot?