Congruent Triangle Proofs

Front

What is the Reflexive Property in geometry?

Back

The Reflexive Property states that any geometric figure is congruent to itself. For example, if triangle ABC is considered, then AB ≅ AB.

Front

What are Alternate Interior Angles?

Back

Alternate Interior Angles are pairs of angles that are on opposite sides of a transversal and inside the two lines it intersects. If the lines are parallel, these angles are congruent.

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 is the purpose of triangle congruence proofs?

Back

Triangle congruence proofs are used to demonstrate that two triangles are congruent by showing that their corresponding sides and angles are equal.

Front

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

Back

The AAS Congruence 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 is the Side-Side-Side (SSS) Congruence Theorem?

Back

The SSS Congruence Theorem 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 Side-Angle-Side (SAS) Congruence Theorem?

Back

The SAS Congruence Theorem 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 Angle-Side-Angle (ASA) Congruence Theorem?

Back

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

Front

What is the significance of corresponding parts of congruent triangles?

Back

The corresponding parts of congruent triangles are equal, which means that if two triangles are proven to be congruent, all their corresponding sides and angles are also congruent.

Front

What is the definition of a transversal in geometry?

Back

A transversal is a line that intersects two or more lines at different points. It creates angles that can be classified as corresponding, alternate interior, and alternate exterior.