Geometry Congruent Triangle Proofs

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if they have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What is the SAS (Side-Angle-Side) Congruence Postulate?

Back

The SAS Postulate states that if two sides of one triangle are congruent to two sides of another triangle and the included angle is also congruent, then the triangles are congruent.

Front

What is the ASA (Angle-Side-Angle) Congruence Postulate?

Back

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

Front

What is the SSS (Side-Side-Side) Congruence Postulate?

Back

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

Front

What is the AAS (Angle-Angle-Side) Congruence Theorem?

Back

The AAS Theorem 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 CPCTC stand for?

Back

CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent.

Front

What is the HL (Hypotenuse-Leg) Theorem?

Back

The HL Theorem 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

If two angles of one triangle are equal to two angles of another triangle, what can be concluded?

Back

The two triangles are similar, and if one side is also equal, they are congruent.

Front

What is the significance of a perpendicular line in triangle proofs?

Back

A perpendicular line creates right angles, which can be used to establish congruence through the use of the right triangle properties.

Front

How can you prove that two triangles are congruent using the SSS postulate?

Back

Measure all three sides of both triangles. If all three sides of one triangle are equal to the corresponding sides of the other triangle, then the triangles are congruent.