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5-5 & 5-6 SSS, SAS, ASA, & AAS

5-5 & 5-6 SSS, SAS, ASA, & AAS. Proving Triangles Congruent. F. B. A. C. E. D. The Idea of a Congruence. Two geometric figures with exactly the same size and shape. How much do you need to know. . . . . . about two triangles to prove that they

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5-5 & 5-6 SSS, SAS, ASA, & AAS

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  1. 5-5 & 5-6 SSS, SAS, ASA, & AAS

  2. Proving Triangles Congruent

  3. F B A C E D The Idea of a Congruence Two geometric figures with exactly the same size and shape.

  4. How much do you need to know. . . . . . about two triangles to prove that they are congruent?

  5. Corresponding Parts • AB DE • BC EF • AC DF •  A  D •  B  E •  C  F B A C E F D You learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. ABC DEF

  6. SSS SAS ASA AAS Do you need all six ? NO !

  7. Side-Side-Side (SSS) E B F A D C • AB DE • BC EF • AC DF ABC DEF

  8. Side-Angle-Side (SAS) B E F A C D • AB DE • A D • AC DF ABC DEF included angle

  9. Included Angle The angle between two sides H G I

  10. E Y S Included Angle Name the included angle: YE and ES ES and YS YS and YE E S Y

  11. Angle-Side-Angle (ASA) B E F A C D • A D • AB  DE • B E ABC DEF included side

  12. Included Side The side between two angles GI GH HI

  13. E Y S Included Side Name the included side: Y and E E and S S and Y YE ES SY

  14. Angle-Angle-Side (AAS) B E F A C D • A D • B E • BC  EF ABC DEF Non-included side

  15. Warning: No SSA Postulate There is no such thing as an SSA postulate! E B F A C D NOT CONGRUENT

  16. Warning: No AAA Postulate There is no such thing as an AAA postulate! E B A C F D NOT CONGRUENT

  17. SSS correspondence • ASA correspondence • SAS correspondence • AAS correspondence • SSA correspondence • AAA correspondence The Congruence Postulates

  18. Name That Postulate (when possible) SAS ASA SSA SSS

  19. Name That Postulate (when possible) AAA ASA SSA SAS

  20. Name That Postulate (when possible) Vertical Angles Reflexive Property SAS SAS Reflexive Property Vertical Angles SSA SAS

  21. HW: Name That Postulate (when possible)

  22. HW: Name That Postulate (when possible)

  23. Let’s Practice ACFE Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: B D For SAS: AF For AAS:

  24. HW Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS: For AAS:

  25. Write a congruence statement for each pair of triangles represented. D B C A E F

  26. 1-1a Slide 1 of 2

  27. 1-1b Slide 1 of 2

  28. 5.6 ASA and AAS

  29. C Y A B X Z Before we start…let’s get a few things straight INCLUDED SIDE

  30. Angle-Side-Angle (ASA) Congruence Postulate A A S S A A Two angles and the INCLUDED side

  31. A A A A S S Angle-Angle-Side (AAS) Congruence Postulate Two Angles and One Side that is NOT included

  32. SSS SAS ASA AAS Your Only Ways To Prove Triangles Are Congruent

  33. Things you can mark on a triangle when they aren’t marked. Overlapping sides are congruent in each triangle by the REFLEXIVE property Alt Int Angles are congruent given parallel lines Vertical Angles are congruent

  34. Ex 1 DEF NLM

  35. D L M F N E Ex 2 What other pair of angles needs to be marked so that the two triangles are congruent by AAS?

  36. D L M F N E Ex 3 What other pair of angles needs to be marked so that the two triangles are congruent by ASA?

  37. G K I H J Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible. Ex 4 ΔGIH ΔJIK by AAS

  38. B A C D E Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible. Ex 5 ΔABC ΔEDC by ASA

  39. Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible. Ex 6 E A C B D ΔACB ΔECD by SAS

  40. Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible. Ex 7 J K L M ΔJMK ΔLKM by SAS or ASA

  41. Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible. Ex 8 J T L K V U Not possible

  42. 1-2a Slide 2 of 2

  43. 1-2b Slide 2 of 2

  44. 1-2b Slide 2 of 2

  45. 1-2c Slide 2 of 2

  46. (over Lesson 5-5) 1-1a Slide 1 of 2

  47. (over Lesson 5-5) 1-1b Slide 1 of 2

  48. 1-1a Slide 1 of 2

  49. 1-1b Slide 1 of 2

  50. 1-1b Slide 1 of 2

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