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5-Minute Check on Lesson 6-2

Transparency 6-3. 5-Minute Check on Lesson 6-2. Determine whether the triangles are similar. Justify your answer. The quadrilaterals are similar. Write a similarity statement and find the scale factor of the larger to the smaller quadrilateral. The triangles are similar. Find x and y.

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5-Minute Check on Lesson 6-2

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  1. Transparency 6-3 5-Minute Check on Lesson 6-2 • Determine whether the triangles are similar.Justify your answer. • The quadrilaterals are similar. Write a similarity statement and find the scale factor of the larger to the smaller quadrilateral. • The triangles are similar. Find x and y. Yes: corresponding angles corresponding sides have same proportion ABCD ~ HGFE Scale factor = 3:2 x = 8.5, y = 9.5 Click the mouse button or press the Space Bar to display the answers.

  2. Lesson 6-3 Similar Triangles

  3. Vocabulary • None new

  4. Objectives • Identify similar triangles • Use similar triangles to solve problems

  5. A P Q B C R AA Triangle Similarity Third angle must be congruent as well(∆ angle sum to 180°) From Similar Triangles Corresponding Side Scale Equal AC AB BC ---- = ---- = ---- PQ PR RQ If Corresponding Angles Of Two Triangles Are Congruent, Then The Triangles Are Similar mA = mP mB = mR

  6. A P Q B C R SSS Triangle Similarity From Similar Triangles Corresponding Angles Congruent A  P B  R C  Q If All Three Corresponding Sides Of Two Triangles Have Equal Ratios, Then The Triangles Are Similar AC AB BC ---- = ---- = ---- PQ PR RQ

  7. A P Q B C R SAS Triangle Similarity If The Two Corresponding Sides Of Two Triangles Have Equal Ratios And The Included Angles Of The Two Triangles Are Congruent, Then The Triangles Are Similar AC AB ---- = ---- and A  P PQ PR

  8. Example 1 In the figure, AB // DC, BE = 27, DE= 45, AE = 21, and CE = 35. Determine which triangles in the figure are similar. Since AB ‖ DC, then BAC  DCE by the Alternate Interior Angles Theorem. Vertical angles are congruent, so BAE  DEC. Answer: Therefore, by the AA Similarity Theorem, ∆ABE  ∆CDE

  9. Answer: I Example 2 In the figure, OW = 7, BW = 9, WT = 17.5, and WI = 22.5. Determine which triangles in the figure are similar.

  10. Since because they are alternate interior angles. By AA Similarity, Using the definition of similar polygons, Example 3 ALGEBRA: Given RS // UT, RS=4, RQ=x+3, QT=2x+10, UT=10, find RQ and QT

  11. Answer: Example 3 cont Substitution Cross products Distributive Property Subtract 8x and 30 from each side. Divide each side by 2. Now find RQ and QT.

  12. Answer: Example 4 ALGEBRA Given AB // DE, AB=38.5, DE=11, AC=3x+8, and CE=x+2, find AC and CE.

  13. Summary & Homework • Summary: • AA, SSS and SAS Similarity can all be used to prove triangles similar • Similarity of triangles is reflexive, symmetric, and transitive • Homework: • Page 301 ( 4-8, 10-21)

  14. Ratios: 1) 2) 3) 4) Similar Polygons Similar Triangles (determine if similar and list in proper order) QUIZ Prep x 12 3 4 x + 7 -4 x - 12 6 = = 14 10 x + 2 5 = 28 z 7 3 = B H K 10 4 A B G N A 6 10 8 y + 1 12 x + 1 M 5 D C W 16 C D J L x - 3 P x + 3 W E V A 6 35° S Z T C 40° 1 Q 11x - 2 85° F B R S W

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