Triangle Congruence Theorems

Front

What is the SSS Congruence Postulate?

Back

The SSS (Side-Side-Side) Congruence Postulate states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

Front

What is the SAS Congruence Postulate?

Back

The SAS (Side-Angle-Side) Congruence Postulate states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.

Front

What is the ASA Congruence Postulate?

Back

The ASA (Angle-Side-Angle) Congruence Postulate states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.

Front

What is the AAS Congruence Theorem?

Back

The AAS (Angle-Angle-Side) Congruence Theorem states that if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.

Front

What additional information is required for two triangles to be congruent by SSS?

Back

No additional information is required; if all three sides are equal, the triangles are congruent.

Front

How can you determine if two triangles are congruent?

Back

You can determine if two triangles are congruent by using one of the congruence postulates: SSS, SAS, ASA, or AAS.

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if they have the same size and shape, meaning their corresponding sides and angles are equal.

Front

If two triangles have two equal angles, what can be said about their sides?

Back

If two triangles have two equal angles, the sides opposite those angles are proportional, and the triangles are similar.

Front

What is the importance of the included angle in the SAS postulate?

Back

The included angle is crucial in the SAS postulate because it must be between the two sides being compared for the triangles to be congruent.

Front

Can two triangles be congruent if only one side is equal?

Back

No, two triangles cannot be congruent if only one side is equal; at least two sides and the included angle must be equal.