Triangle Congruence Statements

Front

What does it mean when we say ∆ABC≅∆XYZ?

Back

It means that triangle ABC is congruent to triangle XYZ, indicating that their corresponding sides and angles are equal.

Front

If AB≅XY, what can we conclude about the triangles ∆ABC and ∆XYZ?

Back

The sides AB and XY are equal in length, which is a part of the congruence condition for the triangles.

Front

What is the definition of congruent triangles?

Back

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

Front

If ∆PIG≅∆COW, what does WO≅?

Back

WO is equal to GI, as corresponding sides of congruent triangles are equal.

Front

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

Back

The SSS Congruence Postulate states that 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

The ASA 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 triangles are congruent.

Front

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

Back

The SAS 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 triangles are congruent.

Front

If ∆ISR ≅ ∆TRS, what can we say about the corresponding triangles?

Back

The corresponding sides and angles of triangles ISR and TRS are equal.

Front

What is the Angle-Angle (AA) Similarity Postulate?

Back

The AA Similarity Postulate states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar, but not necessarily congruent.

Front

If ∆JIK≅∆TSR, what does this imply about the sides and angles?

Back

It implies that the corresponding sides and angles of triangles JIK and TSR are equal.