Congruent Triangle Theorems

Front

What is the definition of congruent triangles?

Back

Triangles that have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What does the SSS Congruence Postulate 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 Congruence Postulate 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 Congruence Postulate 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 Congruence Theorem state?

Back

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 triangles are congruent.

Front

What does the HL Congruence Theorem state?

Back

If the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Front

What is a congruence statement?

Back

A statement that indicates that two geometric figures are congruent, typically written in the form ΔABC ≅ ΔDEF.

Front

How can you determine if two triangles are congruent using the SSS Postulate?

Back

Measure the lengths of all three sides of both triangles; if all three pairs of corresponding sides are equal, the triangles are congruent.

Front

What is the significance of corresponding parts in congruent triangles?

Back

Corresponding parts of congruent triangles are equal, meaning that if triangles are congruent, their corresponding sides and angles are also equal.

Front

What is the relationship between congruent triangles and their angles?

Back

If two triangles are congruent, then their corresponding angles are also equal.