Triangle Congruence Statements

Front

What is the definition of triangle congruence?

Back

Triangle congruence means that two triangles are congruent if they have the same size and shape, which can be proven using various congruence criteria.

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

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, which states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, which 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

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, which 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 does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, which 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 triangles are congruent.

Front

What does HL stand for in triangle congruence?

Back

HL stands for Hypotenuse-Leg, which is a criterion for proving the congruence of right triangles. It states that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Front

If ∆ABC ≅ ∆XYZ, what can we conclude about the corresponding sides?

Back

If ∆ABC ≅ ∆XYZ, then AB ≅ XY, BC ≅ YZ, and AC ≅ XZ.

Front

If ∆ABC ≅ ∆LMN, which statement is NOT true?

Back

The statement that is NOT true is BC ≅ ML.

Front

Given ∆ABC ≅ ∆XYZ, what can we say about the angles?

Back

If ∆ABC ≅ ∆XYZ, then ∠A ≅ ∠X, ∠B ≅ ∠Y, and ∠C ≅ ∠Z.