1. Proving Triangles Congruent

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

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

4. 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 1.AB  DE 2.BC  EF 3.AC  DF 4.  A   D 5.  B   E 6.  C   F

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

6. Side-Side-Side (SSS) 1. AB  DE 2. BC  EF 3. AC  DF  ABC   DEF B A C E D F

7. Side-Angle-Side (SAS) 1. AB  DE 2.  A   D 3. AC  DF  ABC   DEF B A C E D F included angle

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

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

10. Angle-Side- Angle (ASA) 1.  A   D 2. AB  DE 3.  B   E  ABC   DEF B A C E D F include d side

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

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

13. Angle-Angle-Side (AAS) 1.  A   D 2.  B   E 3. BC  EF  ABC   DEF B A C E D F Non-included side

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

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

16. The Congruence Postulates  SSS correspondence  ASA correspondence  SAS correspondence  AAS correspondence  SSA correspondence  AAA correspondence

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

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

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

20. HW: Name That Postulate (when possible)

21. HW: Name That Postulate

22. 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 A  F AC  FE

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

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