Triangle Congruence Theorems

Front

What is the AAA triangle congruence theorem?

Back

AAA (Angle-Angle-Angle) states that if two triangles have three angles that are congruent, the triangles are similar, but not necessarily congruent.

Front

What does the SAS triangle congruence theorem state?

Back

SAS (Side-Angle-Side) states that 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 is the AAS triangle congruence theorem?

Back

AAS (Angle-Angle-Side) states that 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 the SSS triangle congruence theorem state?

Back

SSS (Side-Side-Side) states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Front

What is the HL triangle congruence theorem?

Back

HL (Hypotenuse-Leg) states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Front

Which triangle congruence theorem is not valid for proving congruence?

Back

AAA (Angle-Angle-Angle) is not a valid theorem for proving triangle congruence, as it only proves similarity.

Front

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

Back

To prove triangles are congruent by ASA (Angle-Side-Angle), you need two angles and the included side to be congruent.

Front

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

Back

To prove triangles are congruent by AAS (Angle-Angle-Side), you need two angles and a non-included side to be congruent.

Front

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

Back

To prove triangles are congruent by SAS (Side-Angle-Side), you need two sides and the included angle to be congruent.

Front

What is the difference between SSA and other congruence theorems?

Back

SSA (Side-Side-Angle) does not guarantee triangle congruence, as it can lead to ambiguous cases.