This document discusses different ways to prove that two triangles are congruent using congruence postulates. It explains that triangles are congruent if corresponding parts are congruent, but you do not need all six. There are four main postulates covered: side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), and angle-angle-side (AAS). It warns that there is no side-side-angle (SSA) or angle-angle-angle (AAA) postulate to prove congruence.

2. Proving Triangles Congruent By Deepak Kumar

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

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

5. In Lesson 4.2, you learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. Corresponding Parts  ABC   DEF B A C E D F AB  DE BC  EF AC  DF  A   D  B   E  C   F

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

21. HW: Name That Postulate (when possible)

22. (when possible) HW: Name That Postulate

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

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