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Congruent triangles have congruent sides and congruent angles.

Congruent Triangles. Congruent triangles have congruent sides and congruent angles. The parts of congruent triangles that “match” are called corresponding parts. Complete each congruence statement. B. A. C. D. F. DEF. E. Complete each congruence statement. B. A. C. E. D. ECD.

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Congruent triangles have congruent sides and congruent angles.

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  1. Congruent Triangles Congruent triangles have congruent sides and congruent angles. The parts of congruent triangles that “match” are called corresponding parts.

  2. Complete each congruence statement. B A C D F DEF E

  3. Complete each congruence statement. B A C E D ECD

  4. Complete each congruence statement. T G K H GTK

  5. CPCTC CorrespondingParts of CongruentTriangles are Congruent

  6. O C D G T A Fill in the blanks O If CAT  DOG, then A  ___ because ________. CPCTC

  7. If XYZ  ABC, then ___ and Y  ___ because _______. Fill in the blanks If FJH  QRS, then ___ and F  ___ because _______. Q CPCTC CPCTC B

  8. Congruence of Triangles

  9. Overlapping sides are congruent in each triangle by the REFLEXIVE property Alt Int Angles are congruent given parallel lines Vertical Angles are congruent

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

  11. Side-Side-Side (SSS) Congruence Postulate 4 4 5 5 6 6 All Three sides in one triangle are congruent to all three sides in the other triangle

  12. Side-Angle-Side (SAS) Congruence Postulate Two sides and the INCLUDED angle

  13. Example #1 DFE UVW by ____ SSS

  14. Example #2 R S Y X T Z Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. ΔRST ΔYZX by SSS

  15. Example #3 R B C A T S Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. Not congruent. Not enough Information to Tell

  16. Example #4 Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. P R Q S ΔPQSΔPRS by SAS

  17. Example #5 Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. P S U Q R T ΔPQRΔSTU by SSS

  18. Example #6 Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. M P R Q N Not congruent. Not enough Information to Tell

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

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

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

  22. SSS SAS ASA AAS NO BAD WORDS Your Only Ways To Prove Triangles Are Congruent

  23. Example #1 DEF NLM by ____ ASA

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

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

  26. G K I H J Determine 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. Example #4 ΔGIH ΔJIK by AAS

  27. 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. Example #5 ΔABC ΔEDC by ASA

  28. 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. Example #6 E A C B D ΔACB ΔECD by SAS

  29. 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. Example #7 J T L K V U Not possible

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