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 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 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 SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a theorem stating that if all three sides of one triangle are equal to all three sides 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

What is the significance of the SSA condition in triangle congruence?

Back

SSA (Side-Side-Angle) does not guarantee triangle congruence, as it can lead to ambiguous cases where two different triangles can be formed.

Front

If two triangles have two sides of equal length and the included angle is also equal, what theorem can be used to prove they are congruent?

Back

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

Front

If two triangles have two angles and the side opposite one of the angles is equal, which theorem applies?

Back

The AAS (Angle-Angle-Side) theorem applies to prove the triangles are congruent.

Front

What is the relationship between the angles in congruent triangles?

Back

In congruent triangles, corresponding angles are equal.

Front

What is the relationship between the sides in congruent triangles?

Back

In congruent triangles, corresponding sides are equal.