1. Triangle Congruence

2. Proving Triangles Congruent

3. Side-Side-Side (SSS) Postulate

4. Side-Angle-Side (SAS) Postulate

5. Non-example of SAS
Why can’t we use SAS to show these triangles congruent?
The angle in the second triangle is not between the two sides! Not SAS!

6. Angle-Side-Angle (ASA) Postulate

7. Assumptions Sometimes we have to mark assumptions
Assumptions are things that we know are true, but the figure might not immediately give us this information for free – we have to think about it!

8. Assumption #1 – Reflexive Property
If two triangles share a side, that side is congruent to itself!
SSS

9. Assumption #2 – Third Angle
If two pairs of corresponding angles are congruent, then the third pair is also congruent!
Why? Triangle Angle Sum Theorem says the measures of the angles have to sum to 180!
ASA

10. Assumption #3 – Vertical Angles
Vertical angles are congruent!
ASA

11. Assumption #4 – Third Side of a RIGHT Triangle
If two pairs of corresponding sides are congruent in a RIGHT TRIANGLE, then the third pair is also congruent!
Why? Pythagorean Theorem states that a2+b2=c2. This can only be true if a, b, and c are the same in both triangles.
SSS