If one pair of opposite sides of a quadrilateral is both congruent and parallel, then it is a parallelogram.

Given: and

Prove: Quadrilateral H K I J is a parallelogram.

Paragraph Proof: We are given that and . Diagonals and are drawn intersecting at point L. and because __(1)__ are congruent. This allows us to prove that by __(2)__. This allows us to state that and because __(3)__. In other words, diagonals and __(4)__ each other by the definition of bisector. According to Theorem 5-7, quadrilateral HKIJ is a parallelogram because the diagonals and bisect each other.

Given: and

Prove: Quadrilateral H K I J is a parallelogram.

Paragraph Proof: We are given that and . Diagonals and are drawn intersecting at point L. and because __(1)__ are congruent. This allows us to prove that by __(2)__. This allows us to state that and because __(3)__. In other words, diagonals and __(4)__ each other by the definition of bisector. According to Theorem 5-7, quadrilateral HKIJ is a parallelogram because the diagonals and bisect each other.

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