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 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 SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a postulate that states if all three sides of one triangle are congruent to all 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 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 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 one right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Front

What is the difference between AAS and ASA?

Back

AAS involves two angles and a non-included side, while ASA involves two angles and the included side.

Front

Can SSA prove triangle congruence?

Back

No, SSA (Side-Side-Angle) does not guarantee triangle congruence; it can lead to ambiguous cases.

Front

If two triangles have two pairs of congruent angles, what can be concluded?

Back

The triangles are congruent by the AAS or ASA postulate.

Front

If two triangles have two pairs of congruent sides and the included angle, what can be concluded?

Back

The triangles are congruent by the SAS postulate.

Front

If two triangles have three pairs of congruent sides, what can be concluded?

Back

The triangles are congruent by the SSS postulate.