Congruent Triangles

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a criterion for triangle congruence 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 criterion for triangle congruence that states if all three sides of one triangle are congruent to all 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 criterion for triangle congruence 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 criterion for triangle congruence 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 SSA stand for in triangle congruence?

Back

SSA stands for Side-Side-Angle, which is NOT a valid criterion for triangle congruence because it does not guarantee that the triangles are congruent.

Front

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

Back

The triangles are similar, but not necessarily congruent unless the sides are also proportional.

Front

What is the significance of the included angle in SAS?

Back

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

Front

Can two triangles be congruent if they have two pairs of congruent sides and a non-included angle?

Back

No, this is an SSA condition, which does not guarantee congruence.

Front

What is the difference between congruent and similar triangles?

Back

Congruent triangles have the same size and shape (all corresponding sides and angles are equal), while similar triangles have the same shape but not necessarily the same size (corresponding angles are equal, and corresponding sides are proportional).

Front

What additional information is needed to prove triangles are congruent by AAS?

Back

You need to know one pair of corresponding sides is congruent along with two pairs of corresponding angles.