Triangle Congruence Theorems

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a theorem that states 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 SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a theorem that states 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 that states 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 that applies 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 definition of congruent figures?

Back

Congruent figures have the same dimensions (side lengths and angle measures), are the same shape and size, and can be mapped onto one another using rigid motions.

Front

What is the SSA condition in triangle congruence?

Back

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

Front

What is the AAA condition in triangle congruence?

Back

AAA stands for Angle-Angle-Angle, which indicates that triangles are similar but not necessarily congruent.

Front

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

Back

The triangles are similar, but not necessarily congruent, as the third side may differ.

Front

What is the significance of the included angle in SAS?

Back

In SAS, the included angle is the angle formed between the two sides being compared, which is crucial for establishing congruence.

Front

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

Back

No, knowing only one side is not sufficient to prove congruence; additional information about angles or other sides is needed.