Triangle Congruence Theorems

Front

What are congruent figures?

Back

Congruent figures have the same dimensions (side lengths and angle measures), are the same shape and size, and can be mapped onto one another using rigid motions.

Front

Which triangle congruence theorem is used to prove triangles are congruent when one leg and the hypotenuse of a right triangle are known?

Back

HL (Hypotenuse-Leg) theorem.

Front

Which triangle congruence theorem is used when two sides and the included angle are known?

Back

SAS (Side-Angle-Side) theorem.

Front

Which triangle congruence theorem is used when all three sides of a triangle are known?

Back

SSS (Side-Side-Side) theorem.

Front

Which triangle congruence theorem is used when two angles and the included side are known?

Back

ASA (Angle-Side-Angle) theorem.

Front

Which triangle congruence theorem is used when two angles and a non-included side are known?

Back

AAS (Angle-Angle-Side) theorem.

Front

What does the SSS theorem state?

Back

If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

Front

What does the SAS theorem state?

Back

If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.

Front

What does the ASA theorem state?

Back

If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.

Front

What does the AAS theorem state?

Back

If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.