Triangle Congruence Theorems

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a theorem that states 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 SSS stand for in triangle congruence?

Back

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

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a theorem 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

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a theorem that states 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 does HL stand for in triangle congruence?

Back

HL stands for Hypotenuse-Leg, a theorem that applies to right triangles, stating that if the hypotenuse and one leg of a 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 triangle congruence theorems?

Back

Triangle congruence theorems are significant because they provide criteria to determine if two triangles are congruent, which is essential in solving geometric problems and proofs.

Front

Can SSA be used to prove triangle congruence?

Back

No, SSA (Side-Side-Angle) cannot be used to prove triangle congruence because it does not guarantee that the triangles are congruent.

Front

If two triangles have two sides of equal length and the included angle is also equal, what theorem can be applied?

Back

The SAS (Side-Angle-Side) theorem can be applied to prove that the triangles are congruent.

Front

If two triangles have three sides of equal length, what theorem can be applied?

Back

The SSS (Side-Side-Side) theorem can be applied to prove that the triangles are congruent.

Front

If two triangles have two angles and the side opposite one of the angles is equal, what theorem can be applied?

Back

The AAS (Angle-Angle-Side) theorem can be applied to prove that the triangles are congruent.