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Triangle Congruence

Triangle Congruence. Geometry Honors. Exploration. Postulate. Side-Side-Side (SSS) Postulate – If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. . R. RAT  PEN. P. A. E. T. N. Postulate.

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Triangle Congruence

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  1. Triangle Congruence Geometry Honors

  2. Exploration

  3. Postulate Side-Side-Side (SSS) Postulate – If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. R RAT  PEN P A E T N

  4. Postulate Side-Angle-Side (SAS) Postulate – If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. D DOG  CAT C G T O A

  5. Starting a Proof Which postulate, if any, could you use to prove that the two triangles are congruent? Q SSS Write a valid congruence statement. P Z ZQPZWP W

  6. Starting a Proof Which postulate, if any, could you use to prove that the two triangles are congruent? R K U T C Not congruent

  7. Starting a Proof Which postulate, if any, could you use to prove that the two triangles are congruent? P SAS Write a valid congruence statement. N L A PANAPL

  8. Starting a Proof Which postulate, if any, could you use to prove that the two triangles are congruent? SSS or SAS H Write a valid congruence statement. E F G I F is the midpoint of HI. EFIGFH

  9. Starting a Proof What other information, if any, do you need to prove the 2 triangles are congruent by SSS or SAS? D A B E C

  10. Starting a Proof What other information, if any, do you need to prove the 2 triangles are congruent by SSS or SAS? M D L N E F

  11. Starting a Proof What other information, if any, do you need to prove the 2 triangles are congruent by SSS or SAS? A N M P T U

  12. A Given: X is the midpoint of AG and of NR. R X N Prove: ANX  GRX G 1. Vertical Angle Theorem 1. AXN GXR 2. Given 2. X is the midpoint of AG 3. AX  XG 3. Def. of midpoint 4. Given 4. X is the midpoint of NR 5. Def. of midpoint 5. NX  XR 6. SAS Postulate 6. ANX GRX

  13. Homework • Ways to Prove Triangles Congruent Worksheet • Ways to Prove Triangles Congruent #2 Worksheet

  14. Exploration

  15. Postulate Angle–Side-Angle (ASA) Postulate – If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. B A BIG  ART I R T G

  16. Which two triangles are congruent? E G P N U A T Write a valid congruence statement. B D

  17. Theorem Angle-Angle-Side (AAS) Theorem – If two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle, then the two triangles are congruent. M B A BOY  MAD O D Y

  18. Q Given: XQ TR, XR bisects QT X M R Prove: XMQ  RMT T 1. Given 1. XQ TR 2. Alt. Int. ’s Theorem 2. X  R 3. XMQ  RMT 3. Vertical Angle Theorem 4. Given 4. XR bisects QT 5. Def. of bisect 5. QM  TM 6. AAS Theorem 6. XMQ RMT

  19. Let’s do the Conclusion Worksheet together.

  20. Homework • Conclusions Worksheet #2

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