Congruent Triangle Proofs

Front

What is the definition of congruent triangles?

Back

Congruent triangles are triangles that are identical in shape and size, meaning their corresponding sides and angles are equal.

Front

What does the Reflexive Property state?

Back

The Reflexive Property states that any geometric figure is congruent to itself, i.e., for any triangle ABC, triangle ABC ≌ triangle ABC.

Front

What is the SAS (Side-Angle-Side) congruence criterion?

Back

The SAS criterion 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 is the AAS (Angle-Angle-Side) congruence criterion?

Back

The AAS criterion 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 is the ASA (Angle-Side-Angle) congruence criterion?

Back

The ASA criterion 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

Which triangle congruence criterion is NOT valid?

Back

The SSA (Side-Side-Angle) criterion is not a valid criterion for triangle congruence.

Front

What is the Vertical Angles Theorem?

Back

The Vertical Angles Theorem states that vertical angles are congruent.

Front

What is the significance of the Reflexive Property in triangle proofs?

Back

The Reflexive Property is often used to show that a side or angle is congruent to itself, which is essential in proving triangles congruent.

Front

How can you prove two triangles are congruent using AAS?

Back

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

Front

What is the relationship between alternate interior angles when two parallel lines are crossed by a transversal?

Back

Alternate interior angles are congruent when formed by parallel lines crossed by a transversal.