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Understanding Congruent Triangles in Geometry

Learn about congruent triangles, corresponding parts, congruence statement, CPCTC, and proof methods like SSS, SAS, AAS. Explore different ways to prove triangles are congruent.

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Understanding Congruent Triangles in Geometry

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  1. Warm up Solve. 1. 40 4x – 20 x 2. 42 2y + 28 3y – 14°

  2. Congruent Triangles

  3. Congruent Triangles Congruent triangles have 3 congruent sides and 3 congruent angles. The parts of congruent triangles that “match” are called corresponding parts.

  4. Congruence Statement In a congruence statement ORDER MATTERS!!!! Everything matches up.

  5. CPCTC Corresponding Parts of Congruent Triangles are Congruent

  6. Complete each congruence statement. B If ABC  DEF, then BC  ___ EF A C D F E

  7. Complete each congruence statement. B If ABC  DEF, then A  ___ D A C D F E

  8. Complete each congruence statement. B If ABC  DEF, then C  ___ F A C D F E

  9. Fill in the blanks If CAT  DOG, then AC  ___ OD

  10. Fill in the blanks BAT  MON N T  ___ _____  ONM _____  MO NM  ____ ATB BA TB

  11. Fill in the blanks BCA   ____ ____   GFE EGF CAB

  12. Complete the congruence statement. MKL _____   JKN

  13. Complete the congruence statement. ABD _____   CBD

  14. 5 ways to Prove Triangles Congruent

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

  16. Side-Angle-Side (SAS) Congruence Postulate Two sides and the INCLUDED angle (the angle is in between the 2 marked sides)

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

  18. Angle-Side-Angle (ASA) Congruence Postulate A A S S A A Two angles and the INCLUDED side (the side is in between the 2 marked angles)

  19. There is one more way to prove triangles congruent, but it’s only for RIGHT TRIANGLES…Hypotenuse Leg HL

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

  21. 3 markings YOU can add if they aren’t marked already

  22. Share a side Reason: Reflexive Property Vertical Angles Reason: Vertical Angles are congruent

  23. Alternate Interior Angles Reason: Alt. Int angles are congruent

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