Congruent Triangles

Front

What is the definition of congruent triangles?

Back

Congruent triangles are triangles that have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What does the SAS (Side-Angle-Side) congruence theorem state?

Back

The SAS 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 triangles are congruent.

Front

What does the SSS (Side-Side-Side) congruence theorem state?

Back

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

Front

What does the ASA (Angle-Side-Angle) congruence theorem state?

Back

The ASA 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 triangles are congruent.

Front

What does the AAS (Angle-Angle-Side) congruence theorem state?

Back

The AAS 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 triangles are congruent.

Front

What does the HL (Hypotenuse-Leg) theorem state?

Back

The HL 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 triangles are congruent.

Front

How can you prove triangles are congruent using the SAS theorem?

Back

To prove triangles are congruent using the SAS theorem, show that two sides of one triangle are equal to two sides of another triangle and that the angle between those sides is also equal.

Front

How can you prove triangles are congruent using the SSS theorem?

Back

To prove triangles are congruent using the SSS theorem, demonstrate that all three sides of one triangle are equal to all three sides of another triangle.

Front

How can you prove triangles are congruent using the ASA theorem?

Back

To prove triangles are congruent using the ASA theorem, show that two angles and the side between them in one triangle are equal to two angles and the corresponding side in another triangle.

Front

How can you prove triangles are congruent using the AAS theorem?

Back

To prove triangles are congruent using the AAS theorem, show that two angles and a non-included side in one triangle are equal to two angles and the corresponding non-included side in another triangle.