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. 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 HL ASA AAS

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

11. Angle-Side- Angle (ASA) 1.  A   D 2. AB  DE 3.  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 side:  Y and  E  E and  S  S and  Y Included Side SY E YE ES SY

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

15. Warning: No SSA or ASS Postulate A C B D E F NOT CONGRUENT There is no such thing as an SSA or ASS 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  SAS  HL  ASA  AAS  SSA or ASS  AAA

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 Reflexive Property SSA

21. Name That Postulate (when possible) Reflexive Property SSS none SSA AAA

22. (when possible) Name That Postulate Vertical AnglesASA Reflexive Property SSA SAS

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 A  F AC  FE

24. Try it! Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS: For AAS:  N   V MK  TU  M   U

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