Practice Triangle Congruence Theorems

Front

What is the Hypotenuse-Leg (HL) theorem?

Back

The HL theorem states that if in two right triangles, the hypotenuse and one leg of one triangle are congruent to the hypotenuse and one leg of another triangle, then the two triangles are congruent.

Front

What is the Angle-Angle-Side (AAS) theorem?

Back

The AAS theorem states that if in two triangles, 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 two triangles are congruent.

Front

What is the Angle-Side-Angle (ASA) theorem?

Back

The ASA theorem states that if in two triangles, two angles and the included side of one triangle are congruent to two angles and the corresponding included side of another triangle, then the two triangles are congruent.

Front

What is the Side-Angle-Side (SAS) theorem?

Back

The SAS theorem states that if in two triangles, two sides and the included angle of one triangle are congruent to two sides and the corresponding included angle of another triangle, then the two triangles are congruent.

Front

What is the Side-Side-Side (SSS) theorem?

Back

The SSS theorem states that if in two triangles, all three sides of one triangle are congruent to all three sides of another triangle, then the two triangles are congruent.

Front

What is the Side-Side-Angle (SSA) condition?

Back

The SSA condition does not guarantee triangle congruence. It is possible to have two triangles with two sides and a non-included angle that are congruent, but the triangles may not be congruent.

Front

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

Back

To prove triangles are congruent by AAS, you need to know that two angles and a non-included side are congruent.

Front

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

Back

To prove triangles are congruent by ASA, you need to know that two angles and the included side are congruent.

Front

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

Back

To prove triangles are congruent by SAS, you need to know that two sides and the included angle are congruent.

Front

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

Back

To prove triangles are congruent by SSS, you need to know that all three sides are congruent.