A quadrilateral with four right angles

A quadrilateral with two pairs of opposite parallel sides

A quadrilateral with four congruent sides and four congruent angles

A quadrilateral with one pair of parallel sides

A quadrilateral with four right angles

A quadrilateral with two pairs of opposite parallel sides

A quadrilateral with four congruent sides and four congruent angles

A quadrilateral with one pair of parallel sides

A quadrilateral with four right angles

A quadrilateral with two pairs of opposite parallel sides

A quadrilateral with four congruent sides and four congruent angles

A quadrilateral with one pair of parallel sides

A quadrilateral with four right angles

A quadrilateral with two pairs of opposite parallel sides

A quadrilateral with four congruent sides and four congruent angles

A quadrilateral with one pair of parallel sides

A quadrilateral with four right angles

A quadrilateral with two pairs of opposite parallel sides

A quadrilateral with four congruent sides and four congruent angles

A quadrilateral with one pair of parallel sides

A quadrilateral with four right angles

A quadrilateral with two pairs of opposite parallel sides

A quadrilateral with four congruent sides and four congruent angles

A quadrilateral with one pair of parallel sides

Proof:

Proof:

Proof:

Proof:

Proof:

Proof:

Proof:

Proof:

Proof:

Proof:

is a parallelogram (given)

We can add the line across the diagonal

is parallel to

is parallel to (definition of a parallelogram)

(alternate interior angles)

is a common side between and

(By Angle-Side-Angle Theorem)

Because the triangles are congruent we can assume:

,

Therefore and

Proof:

is a parallelogram (given)

We can add the line across the diagonal

is parallel to

is parallel to (definition of a parallelogram)

(corresponding angles)

is a common side between and

(By Angle-Side-Angle Theorem)

(corresponding parts of congruent triangles)

(Addition of equalities)

(Angle Addition Postulate)

Therefore and

Proof:

is a parallelogram (given)

We can add the line across the diagonal

is parallel to

is parallel to (definition of a parallelogram)

(alternate interior angles)

is a common side between and

(By Angle-Side-Angle Theorem)

(corresponding parts of congruent triangles)

(Addition of equalities)

(Angle Addition Postulate)

Therefore and