# Common Core: High School - Geometry : Parallelogram Proofs

## Example Questions

### Example Question #11 : Prove Parallelogram Theorems: Ccss.Math.Content.Hsg Co.C.11

Which of the following is the definition of a parallelogram?

A quadrilateral with four right angles

A quadrilateral with four congruent sides and four congruent angles

A quadrilateral with two pairs of opposite parallel sides

A quadrilateral with one pair of parallel sides

A quadrilateral with two pairs of opposite parallel sides

Explanation:

A parallelogram is a quadrilateral with two pairs of opposite parallel sides such as the following.

Opposite sides of a parallelogram are congruent as well as its opposite angles.

### Example Question #141 : Congruence

Which of the following is the definition of a parallelogram?

A quadrilateral with one pair of parallel sides

A quadrilateral with two pairs of opposite parallel sides

A quadrilateral with four congruent sides and four congruent angles

A quadrilateral with four right angles

A quadrilateral with two pairs of opposite parallel sides

Explanation:

A parallelogram is a quadrilateral with two pairs of opposite parallel sides such as the following.

Opposite sides of a parallelogram are congruent as well as its opposite angles.

### Example Question #3 : Parallelogram Proofs

Which of the following is the definition of a parallelogram?

A quadrilateral with four congruent sides and four congruent angles

A quadrilateral with four right angles

A quadrilateral with two pairs of opposite parallel sides

A quadrilateral with one pair of parallel sides

A quadrilateral with two pairs of opposite parallel sides

Explanation:

A parallelogram is a quadrilateral with two pairs of opposite parallel sides such as the following.

Opposite sides of a parallelogram are congruent as well as its opposite angles.

### Example Question #141 : Congruence

Prove that the following parallelogram has diagonals that prove two congruent triangles.

Proof:

Proof:

Proof:

Proof:

Explanation:

### Example Question #491 : High School: Geometry

Prove that the following parallelogram has four pairs of consecutive supplementary angles.

Proof:

Proof:

Proof:

Proof:

Explanation:

Thus, we have shown that this parallelogram has four pairs of consecutive supplementary angles.

### Example Question #6 : Parallelogram Proofs

Prove the following parallelogram has two pairs of opposite congruent angles.

Proof:

Proof:

Proof:

Proof:

Explanation:

### Example Question #7 : Parallelogram Proofs

Prove the following parallelogram has opposite congruent sides.

Proof:

Proof:

Proof:

Proof:

Explanation:

Thus, we have proven this parallelogram has congruent opposite sides.

### Example Question #2 : Parallelogram Proofs

Prove that since this quadrilateral has two pairs of opposite congruent sides, it is a parallelogram.

Proof:

Proof:

Proof:

Proof:

Explanation:

Thus, we have shown that if a quadrilateral has two pairs of congruent opposite sides, then it is a parallelogram.

### Example Question #9 : Parallelogram Proofs

True or False: Is the following quadrilateral a parallelogram?

False

True

True

Explanation:

This is true because a theorem states that if a quadrilateral has two consecutive angles that are supplementary, then the quadrilateral is a parallelogram.

### Example Question #501 : High School: Geometry

Prove that if the following quadrilateral has a pair of opposite parallel, congruent sides, it is a parallelogram.

Proof:

Proof:

Proof: