SSS SAS ASA AAS HL

Front

What does SSS stand for in triangle congruence?

Back

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

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a postulate stating that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

Front

What does ASA stand for in triangle congruence?

Back

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

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a postulate 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, the triangles are congruent.

Front

What does HL stand for in triangle congruence?

Back

HL stands for Hypotenuse-Leg, a theorem stating that if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, the triangles are congruent.

Front

What is the significance of congruent triangles in geometry?

Back

Congruent triangles have the same size and shape, which means their corresponding sides and angles are equal, allowing for various applications in proofs and real-world problems.

Front

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

Back

No, knowing only one side is not sufficient to prove congruence; at least two sides and the included angle or other combinations must be known.

Front

What is the SSA condition in triangle congruence?

Back

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

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. Both can prove triangle congruence.

Front

How can you determine if triangles are not congruent?

Back

If the corresponding sides and angles do not match according to any of the congruence postulates (SSS, SAS, ASA, AAS, HL), the triangles are not congruent.