1. Proving Triangle Congruency

2. What does it mean for triangles to be congruent? Congruent triangles are identical meaning that their side lengths and angle measurements are exactly the same.

3. How do we prove that 2 triangles are congruent? There are 5 theorems that prove triangle congruency. SSS – side-side-side SAS – side-angle-side ASA – angle-side-angle AAS – angle-angle-side HL – hypotenuse-leg

4. SSS (Side-Side-Side) If all three corresponding sides of the 2 triangles are congruent, then the triangles are congruent.

5. SAS (Side-Angle-Side) If two corresponding sides and the angle in between are congruent, then the 2 triangles are congruent.

6. ASA (Angle-Side-Angle) If 2 corresponding angles and the side in between are congruent, then the 2 triangles are congruent.

7. AAS (Angle-Angle-Side) If 2 corresponding angles and the side that is not in between are congruent, then the 2 triangles are congruent.

8. HL (Hypotenuse-Leg) If the corresponding hypotenuses and legs of 2 right triangles are congruent, then the 2 right triangles are congruent

9. Examples

10. More Examples

11. Even More Examples