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

2. Lesson 6-3 Similar Triangles

3. Vocabulary None new

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

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

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

7. 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 P Q R A B C

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

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

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

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. QUIZ Prep Ratios: 1) 2) 3) 4) Similar Polygons Similar Triangles (determine if similar and list in proper order) AB C D A B C E W A B C D F G HK J L W R Z S T N Q V S P M W x + 2 5 = 14 10 x - 12 6 = x + 7 -4 3434 = x 12 7373 = 28 z 85° 40° 35° x + 3 6 11x - 2 1 12 16 10 y + 1 x - 3 8 x + 1 6 10 5 4