Triangle Congruence Theorems

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 congruent to two angles and the corresponding non-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 that states if three sides of one triangle are congruent to three sides 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 congruent to two sides and the included angle 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 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

Can SSA prove triangle congruence?

Back

No, SSA (Side-Side-Angle) does not prove triangle congruence because it can lead to ambiguous cases where two different triangles can be formed.

Front

Can AAA prove triangle congruence?

Back

No, AAA (Angle-Angle-Angle) does not prove triangle congruence because it only shows that triangles are similar, not necessarily congruent.

Front

If two triangles have two pairs of congruent angles, what can be said about the triangles?

Back

The triangles are similar, but not necessarily congruent.

Front

What is the significance of the included angle in SAS?

Back

In SAS, the included angle is crucial because it is the angle between the two sides being compared, ensuring that the triangles are congruent.

Front

What is the difference between congruent and similar triangles?

Back

Congruent triangles are identical in size and shape, while similar triangles have the same shape but may differ in size.