Ways to Prove 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 triangle congruence?

Back

Triangle congruence means that two triangles are identical in shape and size, meaning all corresponding sides and angles are equal.

Front

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

Back

If two triangles have two pairs of equal angles, they are congruent by the AAS criterion.

Front

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

Back

If two triangles have three pairs of equal sides, they are congruent by the SSS criterion.

Front

If two triangles have two sides and the included angle equal, what can be concluded?

Back

If two triangles have two sides and the included angle equal, they are congruent by the SAS criterion.

Front

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

Back

No, two triangles cannot be proven congruent with only one side equal; at least two sides or angles must be equal.