Triangle Congruence Theorems

Front

What does the ASA triangle congruence theorem state?

Back

The ASA (Angle-Side-Angle) theorem states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.

Front

What does the SSS triangle congruence theorem state?

Back

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

Front

What does the SAS triangle congruence theorem state?

Back

The SAS (Side-Angle-Side) theorem states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.

Front

What does the AAS triangle congruence theorem state?

Back

The AAS (Angle-Angle-Side) theorem states that if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.

Front

What does the HL triangle congruence theorem state?

Back

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

Front

What is the difference between AAS and ASA?

Back

AAS involves two angles and a non-included side, while ASA involves two angles and the included side.

Front

Can AAA be used to prove triangle congruence? Why or why not?

Back

No, AAA (Angle-Angle-Angle) cannot be used to prove triangle congruence because it only shows that the triangles are similar, not necessarily congruent.

Front

What is the significance of the included side in ASA and SAS?

Back

The included side is the side that is between the two angles in ASA and the side that is between the two sides in SAS, which is crucial for establishing congruence.

Front

How can you determine if two triangles are congruent using SSS?

Back

Measure all three sides of both triangles; if all three pairs of corresponding sides are equal, the triangles are congruent.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.