Properties of Congruent Triangles

Front

What are congruent triangles?

Back

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

Front

What is the Side-Side-Side (SSS) Congruence Postulate?

Back

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

Front

What is the Angle-Side-Angle (ASA) Congruence Postulate?

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 is the Side-Angle-Side (SAS) Congruence Postulate?

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 is the Angle-Angle (AA) Similarity Postulate?

Back

If two angles of one triangle are equal to two angles of another triangle, then the triangles are similar, but not necessarily congruent.

Front

What does it mean for two angles to be congruent?

Back

Two angles are congruent if they have the same measure.

Front

What is the definition of corresponding sides in congruent triangles?

Back

Corresponding sides are the sides of two triangles that are in the same relative position.

Front

If ΔABC is congruent to ΔDEF, what can we say about their corresponding angles?

Back

The corresponding angles ∠A, ∠B, ∠C are equal to ∠D, ∠E, ∠F respectively.

Front

What is the definition of a congruence transformation?

Back

A transformation that preserves the size and shape of a figure, such as translation, rotation, or reflection.

Front

How can you prove that two triangles are congruent using the SSS postulate?

Back

By showing that all three pairs of corresponding sides are equal in length.