Two triangles are congruent when three corresponding sides and three corresponding angles are

congruent. However, you do not need to know all the sides and angles are congruent. You need to know

that a combination of three sides or/and angles are congruent.

We proved by construction the postulates SSS (side-side-side), SAS (side-angle-side), and ASA (angle-

side-angle). We also justify the theorems of AAS (angle-angle-side) and the HL (hypotenuse-leg) as

methods to prove triangle congruence.

Below are other combinations and we want to test if it is possible to prove triangle congruence when

only given the provided information.

Angle-Angle-Angle: AAA

can make two unique triangles with three congruent angles.

Can you make more than one unique triangle given three angle measures? Are the triangles formed always

congruent? Explain your reasoning. Show your work.

Side-Side-Angle: SSA

can make two unique triangles with two congruent sides and one congruent angle not

between the two sides.

Can you make more than one unique triangle given two sides and an angle not between them? Are the triangles

formed always congruent? Explain your reasoning. Show your work.