Proofs with Parallelograms

Front

What is a parallelogram?

Back

A parallelogram is a quadrilateral with opposite sides that are both congruent and parallel.

Front

What property states that if two angles are vertical, then they are congruent?

Back

Vertical angles are congruent.

Front

What does the Reflexive Property state?

Back

The Reflexive Property states that any geometric figure is congruent to itself.

Front

What is the ASA congruence postulate?

Back

The ASA (Angle-Side-Angle) 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 SAS congruence postulate?

Back

The SAS (Side-Angle-Side) postulate 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 AAS congruence postulate?

Back

The AAS (Angle-Angle-Side) postulate 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 SSS congruence postulate?

Back

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

Front

What can be concluded if a quadrilateral has one pair of opposite sides that are both congruent and parallel?

Back

The quadrilateral is a parallelogram.

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.

Front

What is the significance of congruent alternate interior angles in parallel lines?

Back

If two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.