Triangle Congruence

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a criterion for triangle congruence where two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle.

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a criterion for triangle congruence where two angles and the included side of one triangle are congruent to the corresponding parts of another triangle.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a criterion for triangle congruence where two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle.

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a criterion for triangle congruence where all three sides of one triangle are congruent to the three sides of another triangle.

Front

Are two triangles with two pairs of congruent angles always congruent?

Back

Yes, two triangles with two pairs of congruent angles are always congruent by the Angle-Angle (AA) similarity theorem, which implies congruence.

Front

If two triangles have one pair of congruent sides and the angles opposite those sides are also congruent, what can be concluded?

Back

The triangles are congruent by the AAS criterion.

Front

How can you determine if two triangles are congruent using the SAS criterion?

Back

To use the SAS criterion, show that two sides of one triangle are congruent to two sides of another triangle and that the included angle between those sides is also congruent.

Front

What is the difference between congruence and similarity in triangles?

Back

Congruence means that two triangles are identical in shape and size, while similarity means that two triangles have the same shape but may differ in size.

Front

Can two triangles be congruent if they have only one pair of congruent sides?

Back

No, having only one pair of congruent sides is not sufficient to prove triangle congruence; additional information about angles or other sides is needed.

Front

What is the significance of the included angle in the SAS criterion?

Back

The included angle is crucial in the SAS criterion because it ensures that the two triangles are not only the same shape but also the same size.