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Similarity Theorems

Similarity Theorems. Similarity in Triangles. Angle-Angle Similarity Postulate (AA~) - If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. W. V. S. 45 . 45 . WRS  BVS because of the AA~ Postulate. R. B.

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Similarity Theorems

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  1. Similarity Theorems

  2. Similarity in Triangles Angle-Angle Similarity Postulate (AA~)- If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. W V S 45 45 WRS  BVS because of the AA~ Postulate. R B

  3. Similarity in Triangles Side-Angle-Side Similarity Postulate (SAS~)- If an angle of one triangle is congruent to an angle of a second triangle, and the sides including the angles are proportional, then the triangles are similar. C T 32 TEA  CUP because of the SAS~ Postulate. 32 28 21 12 16 A E U P The scale factor is 4:3.

  4. Similarity in Triangles Side-Side-Side Similarity Postulate (SSS~)- If the corresponding sides of two triangles are proportional, then the triangles are similar. A 30 15 C B ABC  QRS because of the SSS~ Postulate. 20 Q 6 3 R S The scale factor is 1:5. 4

  5. Are the following triangles similar? If so, what similarity statement can be made. Name the postulate or theorem you used. F J H K G Yes, FGH  KJH because of the AA~ Postulate

  6. Are the following triangles similar? If so, what similarity statement can be made. Name the postulate or theorem you used. G M 3 6 I H 4 O R 10 No, these are not similar because

  7. Are the following triangles similar? If so, what similarity statement can be made. Name the postulate or theorem you used. A 25 20 X Y 25 30 B C No, these are not similar because

  8. Are the following triangles similar? If so, what similarity statement can be made. Name the postulate or theorem you used. A 2 3 P J 3 5 3 B C 8 Yes, APJ  ABC because of the SSS~ Postulate.

  9. Explain why these triangles are similar. Then find the value of x. 4.5 5 x 3 These 2 triangles are similar because of the AA~ Postulate. x=7.5

  10. Explain why these triangles are similar. Then find the value of x. 5 x 110 70 3 3 These 2 triangles are similar because of the AA~ Postulate. x=2.5

  11. Explain why these triangles are similar. Then find the value of x. x 24 14 22 These 2 triangles are similar because of the AA~ Postulate. x=12

  12. Explain why these triangles are similar. Then find the value of x. 6 9 2 x These 2 triangles are similar because of the AA~ Postulate. x= 12

  13. Explain why these triangles are similar. Then find the value of x. 4 5 x 15 These 2 triangles are similar because of the AA~ Postulate. x=8

  14. Explain why these triangles are similar. Then find the value of x. x 7.5 12 18 These 2 triangles are similar because of the AA~ Postulate. x= 15

  15. Please complete the Ways to Prove Triangles Similar Worksheet.

  16. Similarity in Triangles Side Splitter Theorem - If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally. You can either use or T x 5 S U 16 10 R V

  17. Theorem If three parallel lines intersect two transversals, then the segments intercepted are proportional. c d a b

  18. Theorem Triangle Angle Bisector Theorem -If a ray bisects an angle of a triangle, then it divides the opposite side on the triangle into two segments that are proportional to the other two sides of the triangle. A B C D

  19. Please complete pg. 449: 1-24, 31-33.

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