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Similar Triangles

Similar Triangles. Chapter 7-3. Identify similar triangles. Use similar triangles to solve problems. Standards 4.0 Students prove basic theorems involving congruence and similarity . (Key)

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Similar Triangles

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  1. Similar Triangles Chapter 7-3

  2. Identify similar triangles. • Use similar triangles to solve problems. Standards 4.0 Students prove basic theorems involvingcongruence and similarity. (Key) Standard 5.0 Students prove that triangles arecongruent or similar, and they are able to use the concept of corresponding parts of congruent triangles. Lesson 3 MI/Vocab

  3. Triangle Similarity is: Lesson 3 TH2

  4. T E C B W Writing Proportionality Statements 34o Given BTW ~ ETC • Write the Statement of Proportionality • Find mTEC • Find TE and BE 3 20 mTEC = mTBW = 79o 79o 12

  5. K Y J L X Z AA  Similarity Theorem • If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. If K  Y and J  X, then  JKL ~  XYZ.

  6. N M P Q R S T Example • Are these two triangles similar? Why?

  7. B Q A C P R SSS  Similarity Theorem • If the corresponding sides of two triangles are proportional, then the two triangles are similar.

  8. E 6 J 4 H B D 8 9 6 6 14 A 10 12 C F G ABC~ FDE SSS ~ Thm Scale Factor = 3:2 Which of the following three triangles are similar? ABC and FDE? Longest Sides Shortest Sides Remaining Sides

  9. E 6 J 4 H B D 8 9 6 6 14 A 10 12 C F G ABC is not similar to DEF Which of the following three triangles are similar? ABC and GHJ Longest Sides Shortest Sides Remaining Sides

  10. K Y J L X Z SAS  Similarity Theorem • If one angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar. ass Pantograph

  11. S 4 5 P Q 15 12 R T Prove RTS ~ PSQ S  S (reflexive prop.) SPQ  SRT SAS  ~ Thm.

  12. N P 15 12 Q 10 9 R T Are the two triangles similar? NQP  TQR Not Similar

  13. 2 yds 5 yds How far is it across the river? x yards 42 yds 2x = 210 x = 105 yds

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

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

  16. In the figure, OW = 7, BW = 9, WT = 17.5, and WI = 22.5. Determine which triangles in the figure are similar. A.ΔOBW ~ ΔITW B.ΔOBW ~ ΔWIT C.ΔBOW ~ ΔTIW D.ΔBOW ~ ΔITW Lesson 3 CYP1

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

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

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

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

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

  22. Indirect Measurement INDIRECT MEASUREMENTJosh 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? Lesson 3 Ex3

  23. Indirect Measurement 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 Lesson 3 Ex3

  24. Indirect Measurement Simplify. Divide each side by 2. Answer: The Sears Tower is 1452 feet tall. Interactive Lab:Cartography and Similarity Lesson 3 Ex3

  25. 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? A. 196 ft B. 39 ft C. 441 ft D. 89 ft Lesson 3 CYP3

  26. Homework Chapter 7-3 • Pg 400 7 – 17, 21, 31 – 38

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