Triangle Congruence

Proving Triangles Congruent

Side-Side-Side (SSS) Postulate

Side-Angle-Side (SAS) Postulate

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!

Angle-Side-Angle (ASA) Postulate

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!

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

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

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

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