Triangle Congruence Statements

Front

What is a triangle congruence statement?

Back

A triangle congruence statement indicates that two triangles are congruent, meaning they have the same size and shape, and their corresponding sides and angles are equal.

Front

List the criteria for triangle congruence.

Back

1. Side-Side-Side (SSS) Congruence 2. Side-Angle-Side (SAS) Congruence 3. Angle-Side-Angle (ASA) Congruence 4. Angle-Angle-Side (AAS) Congruence 5. Hypotenuse-Leg (HL) Congruence (for right triangles)

Front

If ∆ABC ≅ ∆DEF, what can we conclude about their corresponding parts?

Back

The corresponding sides and angles of the triangles are equal: AB = DE, BC = EF, AC = DF and ∠A = ∠D, ∠B = ∠E, ∠C = ∠F.

Front

What does the notation ∆JIK ≅ ∆TSR signify?

Back

It signifies that triangle JIK is congruent to triangle TSR, meaning they have the same shape and size.

Front

How do you write a congruence statement for triangles?

Back

A congruence statement is written by listing the vertices of the triangles in corresponding order, such as ∆ABC ≅ ∆DEF.

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 two 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 two 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 two triangles are congruent.

Front

What is the Angle-Angle-Side (AAS) Congruence Theorem?

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 two triangles are congruent.

Front

What is the Hypotenuse-Leg (HL) Congruence Theorem?

Back

In right triangles, if the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of another triangle, then the two triangles are congruent.