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Bell Work Wednesday, August 7, 2013

Bell Work Wednesday, August 7, 2013. List two acts that will results in a student having a teacher conference. Standard. Congruency postulates, SSS, SAS, ASA, & AAS. Essential Question. How does learning the congruency postulates help me prove that two triangle are congruent?. Closing.

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Bell Work Wednesday, August 7, 2013

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  1. Bell WorkWednesday, August 7, 2013 List two acts that will results in a student having a teacher conference.

  2. Standard • Congruency postulates, SSS, SAS, ASA, & AAS

  3. Essential Question • How does learning the congruency postulates help me prove that two triangle are congruent?

  4. Closing • See nature by numbers video:http://www.youtube.com/watch?v=kkGeOWYOFoA • Homework Assignment #1 – You saw the video, Nature by Numbers. Submit a picture of something from nature and point out one or several geometric shapes similarly to what you saw in the video. Due: Thursday in class.

  5. The congruence postulates:SSS, SAS, ASA, & AAS

  6. Proving Triangles Congruent

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

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

  9. 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  25. HW: Name That Postulate (when possible)

  26. HW: Name That Postulate (when possible)

  27. 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:

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

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

  30. 1-1A Slide 1 of 2

  31. 1-1B Slide 1 of 2

  32. 5.6 ASA and AAS

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

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

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

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

  37. 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

  38. Ex 1 DEF NLM

  39. 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?

  40. 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?

  41. 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

  42. 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

  43. 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

  44. 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

  45. 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

  46. 1-2A Slide 2 of 2

  47. 1-2B Slide 2 of 2

  48. 1-2B Slide 2 of 2

  49. 1-2C Slide 2 of 2

  50. (over Lesson 5-5) 1-1A Slide 1 of 2

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