Proving a Quadrilateral is a Parallelogram

This lesson focuses on proving a quadrilateral is a parallelogram. It covers various methods such as proving both pairs of opposite sides are parallel or congruent, one pair of opposite sides is both congruent and parallel, both pairs of opposite angles are congruent, consecutive angles are supplementary, and diagonals bisect each other. The lesson includes a detailed proof of the diagonals bisecting each other and concludes with example problems to apply these concepts.

What is the first method to prove a quadrilateral is a parallelogram?

• Prove both pairs of opposite sides are parallel

• Prove both pairs of opposite angles are congruent

• Prove both pairs of opposite sides are congruent

• Prove one pair of opposite sides are both congruent and parallel

According to the first method, what must be true about the opposite sides of a quadrilateral?

• They must be supplementary

• They must be parallel

• They must be congruent

• They must be both congruent and parallel

What is the second method to prove a quadrilateral is a parallelogram?

• Prove both pairs of opposite angles are congruent

• Prove one pair of opposite sides are both congruent and parallel

• Prove both pairs of opposite sides are congruent

• Prove both pairs of opposite sides are parallel

In the second method, what must be true about the opposite sides of a quadrilateral?

• They must be both congruent and parallel

• They must be parallel

• They must be congruent

• They must be supplementary

What is the third method to prove a quadrilateral is a parallelogram?

• Prove both pairs of opposite sides are parallel

• Prove one pair of opposite sides are both congruent and parallel

• Prove both pairs of opposite angles are congruent

• Prove both pairs of opposite sides are congruent

In the third method, what must be true about one pair of opposite sides of a quadrilateral?

• They must be supplementary

• They must be both congruent and parallel

• They must be parallel

• They must be congruent

What is the fourth method to prove a quadrilateral is a parallelogram?

• Prove one pair of opposite sides are both congruent and parallel

• Prove both pairs of opposite angles are congruent

• Prove both pairs of opposite sides are congruent

• Prove both pairs of opposite sides are parallel

What is the fifth method to prove a quadrilateral is a parallelogram?

• Prove an angle is supplementary to both of its consecutive angles

• Prove one pair of opposite sides are both congruent and parallel

• Prove both pairs of opposite sides are congruent

• Prove both pairs of opposite sides are parallel

What is the sixth method to prove a quadrilateral is a parallelogram?

• Prove both pairs of opposite sides are congruent

• Prove both pairs of opposite sides are parallel

• Prove one pair of opposite sides are both congruent and parallel

• Prove the diagonals bisect each other

In the example problem, what additional information is needed to prove that a quadrilateral is a parallelogram if one pair of opposite sides is congruent?

• The angles are congruent

• The sides are parallel

• The angles are supplementary

• The diagonals bisect each other