Triangle Congruence Statements

Front

What is a triangle congruence statement?

Back

A triangle congruence statement asserts that two triangles are congruent, meaning they have the same size and shape, which can be shown using specific criteria such as SSS, SAS, ASA, AAS, or HL.

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for 'Side-Side-Side', a criterion for triangle congruence stating that if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for 'Side-Angle-Side', a criterion for triangle congruence stating that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for 'Angle-Side-Angle', a criterion for triangle congruence stating that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for 'Angle-Angle-Side', a criterion for triangle congruence stating 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, the triangles are congruent.

Front

What does HL stand for in triangle congruence?

Back

HL stands for 'Hypotenuse-Leg', a criterion for triangle congruence applicable to right triangles, stating that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, the triangles are congruent.

Front

If ∆AIG ≅ ∆QOW, what can be concluded about the corresponding sides?

Back

The corresponding sides of the triangles are equal in length, meaning AI = QO, IG = OW, and AG = WQ.

Front

If ∆ABC ≅ ∆LMN, what can be said about the angles?

Back

The corresponding angles of the triangles are equal, meaning ∠A = ∠L, ∠B = ∠M, and ∠C = ∠N.

Front

What is the significance of the order of letters in triangle congruence statements?

Back

The order of letters in triangle congruence statements indicates the correspondence of vertices and sides; for example, if ∆ABC ≅ ∆LMN, then A corresponds to L, B to M, and C to N.

Front

What is a counterexample in the context of triangle congruence?

Back

A counterexample is an example that disproves a statement; for instance, if two triangles have two sides equal but the included angle is not, they are not congruent.