SSS and SAS Proofs

Front

What is the Reflexive Property?

Back

The Reflexive Property states that any geometric figure is congruent to itself. For example, triangle ABC is congruent to triangle ABC.

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, then 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, then the triangles are congruent.

Front

What is the Transitive Property?

Back

The Transitive Property states that if one quantity is equal to a second quantity, and the second quantity is equal to a third quantity, then the first quantity is equal to the third. For example, if A = B and B = C, then A = C.

Front

What is ASA 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, then the triangles are congruent.

Front

What is AAS 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, then the triangles are congruent.

Front

What is HL Congruence?

Back

HL stands for Hypotenuse-Leg, which is a criterion for triangle congruence applicable to 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

What is the significance of congruent triangles?

Back

Congruent triangles have the same size and shape, meaning their corresponding sides and angles are equal. This property is essential in proving various geometric theorems and solving problems.

Front

How can you prove triangles are congruent using SSS?

Back

To prove triangles are congruent using SSS, you must show that all three sides of one triangle are equal to the three sides of another triangle.

Front

How can you prove triangles are congruent using SAS?

Back

To prove triangles are congruent using SAS, you must show that two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.