Proofs and Triangle Congruence

Front

What is the Reflexive Property of Congruence?

Back

The Reflexive Property of Congruence states that any geometric figure is congruent to itself. For example, if triangle ABC is considered, then ⊿ABC ≅ ⊿ABC.

Front

What does the Symmetric Property of Congruence state?

Back

The Symmetric Property of Congruence states that if one figure is congruent to another, then the second figure is congruent to the first. For example, if ⊿ABC ≅ ⊿DEF, then ⊿DEF ≅ ⊿ABC.

Front

Define the Transitive Property of Congruence.

Back

The Transitive Property of Congruence states that if figure A is congruent to figure B, and figure B is congruent to figure C, then figure A is congruent to figure C. For example, if ⊿ABC ≅ ⊿DEF and ⊿DEF ≅ ⊿GHI, then ⊿ABC ≅ ⊿GHI.

Front

What is the Distributive Property?

Back

The Distributive Property states that a(b + c) = ab + ac. It is not directly related to congruence but is a fundamental property in algebra.

Front

What does SSS stand for in triangle congruence?

Back

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

Front

Explain the SAS criterion for triangle congruence.

Back

SAS stands for Side-Angle-Side. It 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 mean in the context of triangle congruence?

Back

ASA stands for Angle-Side-Angle. It is a criterion for triangle congruence that states 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

Define AAS in triangle congruence.

Back

AAS stands for Angle-Angle-Side. It 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 is the HL criterion for triangle congruence?

Back

HL stands for Hypotenuse-Leg. It is a criterion for triangle congruence that applies to right triangles. 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

What is a congruence statement?

Back

A congruence statement is a mathematical statement that indicates that two figures are congruent. For example, ⊿ABC ≅ ⊿DEF means triangle ABC is congruent to triangle DEF.