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', which is 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', which is 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', which is 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', which is 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', which is 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 triangle ∆ABC is congruent to triangle ∆DEF, what can be inferred about their corresponding parts?

Back

If triangle ∆ABC is congruent to triangle ∆DEF, then their corresponding sides and angles are equal: AB = DE, BC = EF, AC = DF, ∠A = ∠D, ∠B = ∠E, ∠C = ∠F.

Front

How do you denote congruence between two triangles?

Back

Congruence between two triangles is denoted using the symbol '≅'. For example, if triangle ∆ABC is congruent to triangle ∆DEF, it is written as ∆ABC ≅ ∆DEF.

Front

What is the significance of the order of letters in a triangle congruence statement?

Back

The order of letters in a triangle congruence statement indicates the correspondence of the vertices. For example, if ∆ABC ≅ ∆DEF, then A corresponds to D, B corresponds to E, and C corresponds to F.

Front

What is the relationship between the angles and sides in congruent triangles?

Back

In congruent triangles, corresponding angles are equal, and corresponding sides are equal in length.