4.3 & 4.4 Proving Triangles

are Congruent

Side-Side-Side (SSS) Congruence Postulate:

If 3 sides of one triangle are congruent to 3 sides of another triangle, then the two triangles are congruent.

Side-Angles-Side (SAS) Congruence Postulate

If 2 sides are congruent and the angle between the sides are congruent then the triangles are congruent.

Angle-Side-Angle (ASA) Congruence Postulate

If 2 angles are congruent and the side between them is congruent then the triangles are congruent.

45

50

45

50

Angle-Angle-Side (AAS) Congruence Theorem

If 2 angles are congruent and the non-included side is congruent then the triangles are congruent.

Overall, the 4 postulates to prove Triangles Congruent

are…• SSS

• SAS

• ASA

• AAS

*Order matters!

Practice Questions:Are the following triangles congruent? If so, by which postulate?

Practice Questions:Name the included angle between side AB and BC:

Practice Questions:Is it possible to prove that the triangles are congruent? If so, state the postulate or theorem you would use.