Proving Triangles Congruent

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a criterion for triangle congruence stating that if three sides of one triangle are equal to three sides of another triangle, 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 stating that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, 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 stating that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a criterion for triangle congruence stating that if two angles and a non-included side of one triangle are equal to two angles and a corresponding non-included side of another triangle, the triangles are congruent.

Front

What does HL stand for in triangle congruence?

Back

HL stands for Hypotenuse-Leg, a criterion for triangle congruence 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, the triangles are congruent.

Front

What is the definition of congruent triangles?

Back

Congruent triangles are triangles that are identical in shape and size, meaning all corresponding sides and angles are equal.

Front

If two triangles have two pairs of equal sides and the included angle is not equal, are they congruent?

Back

No, they are not congruent. The SAS criterion requires the included angle to be equal.

Front

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

Back

No, having only one pair of equal sides is not sufficient for triangle congruence.

Front

What is the importance of triangle congruence in geometry?

Back

Triangle congruence is important because it allows us to prove that two triangles are identical, which is fundamental in solving geometric problems and establishing properties of shapes.

Front

How can you prove that two triangles are not congruent?

Back

You can prove that two triangles are not congruent by showing that at least one pair of corresponding sides or angles is not equal.