1. WHAT IS A CONGRUENT TRIANGLE??

2. Definition Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles are equal in size.

3. What makes a triangle? A triangle is composed of 6 parts: 3 sides 3 angles If all 6 of these parts are congruent to another triangle, then we can say that the two triangles are congruent.

4. Visual/Picture

5. Order Matters!! It is very important to remember that the order of the congruent parts of triangles matters.

6. Examples/Models

7. Non-Examples

8. Congruent Triangle Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles are equal in size.

10. Triangle Congruence SAS, AAS, ASA, SSS, HL

11. Shortcuts to congruence Should we really need to find all 6 parts of a triangle to show they are congruent or can we use shortcuts?

12. Side-Side-Side If two triangles have ALL 3 of the same side lengths, then we can say they are congruent by the SSS postulate side

13. Side-Angle-Side If two triangles have the same side lengths and the same angle measure in-between those sides, the two triangles are congruent by the SAS postulate. side angle side

14. Angle-Side-Angle If two triangles have 2 congruent angles and a congruent side in- between those angles, then they are congruent by the ASA postulate angle side

15. Angle-Angle-Side If two triangles have 2 congruent angles and a congruent side that isn’t in-between them, then the triangles are congruent by the AAS postulate angle side

16. What about Angle-Side-Side? Angle-Side-Side is not enough to prove triangles are congruent. As an easy way to remember that: don’t be an and try to use A.S.S.

17. Hypotenuse-Leg If the hypotenuse and the same leg of two right triangles are congruent then the two right triangles are congruent. hypot leg