Triangle Congruence Theorems

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a postulate that states if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side 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 postulate that states if three sides of one triangle are congruent 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, a postulate that states if two sides and the included angle of one triangle are congruent to two sides and the included angle 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 congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Front

What is the SSA condition in triangle congruence?

Back

SSA stands for Side-Side-Angle, which is not a valid method for proving triangle congruence because it can lead to ambiguous cases.

Front

List the five ways to prove triangles congruent.

Back

The five ways to prove triangles congruent are: SSS, SAS, ASA, AAS, and HL.

Front

What is the ASA postulate in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a postulate that states if two angles and the included side of one triangle are congruent to two angles and the corresponding included side of another triangle, then the triangles are congruent.

Front

What is the difference between AAS and ASA?

Back

AAS (Angle-Angle-Side) involves two angles and a non-included side, while ASA (Angle-Side-Angle) involves two angles and the included side.

Front

Can two triangles be congruent if only two sides are known?

Back

Not necessarily; knowing only two sides (SSA) does not guarantee triangle congruence due to the possibility of different triangle configurations.

Front

What is the significance of congruent triangles in geometry?

Back

Congruent triangles have the same size and shape, which means all corresponding sides and angles are equal, allowing for various geometric proofs and constructions.