1. Triangle Congruence Theorems
Geometry Notes – 4.2/4.3
Mr. Belanger

2. Importance Used to prove triangles congruent
Gives many options for proving congruence
Will continue to be used following this chapter

3. SSS Congruence Theorem
Side – Side – Side Congruence: If three corresponding sides in two triangles are congruent, then the triangles are congruent.

4. SAS Congruence Theorem
Side – Angle – Side Congruence: If, in two triangles, two sides and the included angle (formed by the two sides) are congruent, then the triangles are congruent.

5. ASA Congruence Theorem
Angle – Side – Angle Congruence: If, in two triangles, two angles and the side connecting them are congruent, then the triangles are congruent.

6. AAS Congruence Theorem
Angle – Angle – Side Congruence: If, in two triangles, two angles and the non-included (not between) side are congruent, then the triangles are congruent.

7. Try to decide if the triangles are congruent and if so, why?
Examples:
Try to decide if the triangles are congruent and if so, why?
SAS

8. Try to decide if the triangles are congruent and if so, why?
Examples:
Try to decide if the triangles are congruent and if so, why?
NO! AAA not a congruence theorem
                     
                     
                     

9. Examples:
In triangle ADB and ADC, angle A is congruent to both, side AD is congruent to both and sides BD = CD.
                           
                           
It’s obvious that ADB and ADC are not congruent. Be careful about just matching up any three parts like SSA. It has to be one of the four theorems.

10. Examples:
Are the triangles congruent?
Yes, AAS

11. Now memorize these four theorems!