Proving Triangles Congruent

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a criterion for triangle congruence where two angles and the included side of one triangle are equal to two angles and the included side of another triangle.

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a criterion for triangle congruence where two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a criterion for triangle congruence where two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a criterion for triangle congruence where all three sides of one triangle are equal to all three sides of another triangle.

Front

What does HL stand for in triangle congruence?

Back

HL stands for Hypotenuse-Leg, a criterion for triangle congruence specifically for right triangles, where the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle.

Front

What is the definition of congruent triangles?

Back

Congruent triangles are triangles that are identical in shape and size, meaning all corresponding sides and angles are equal.

Front

When can triangles be considered not congruent?

Back

Triangles can be considered not congruent if none of the congruence criteria (ASA, AAS, SAS, SSS, HL) are satisfied.

Front

What is the Angle-Angle (AA) criterion?

Back

The AA criterion states that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar, but not necessarily congruent.

Front

What is the importance of the included angle in SAS?

Back

In SAS, the included angle is crucial because it is the angle formed between the two sides being compared; without it, the triangles may not be congruent.

Front

Can two triangles be congruent if only one side is equal?

Back

No, two triangles cannot be congruent if only one side is equal; at least two sides and the included angle must be equal (SAS) or two angles and the included side (ASA) or other congruence criteria must be met.