Triangle Congruence Theorems

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a theorem stating that 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 stating that 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 stating that 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 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, then the triangles are congruent.

Front

What does HL stand for in triangle congruence?

Back

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

Front

Can SSA be used to prove triangle congruence?

Back

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

Front

If two triangles have two sides equal and the included angle is also equal, which theorem applies?

Back

The SAS (Side-Angle-Side) theorem applies.

Front

If two triangles have three sides equal, which theorem applies?

Back

The SSS (Side-Side-Side) theorem applies.

Front

If two triangles have two angles and the side between them equal, which theorem applies?

Back

The ASA (Angle-Side-Angle) theorem applies.

Front

If two triangles have two angles and a non-included side equal, which theorem applies?

Back

The AAS (Angle-Angle-Side) theorem applies.