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Quadrilateral Proofs

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**Quadrilateral Classification**

Parallelogram Trapezoid Rectangle Rhombus Isosceles Trapezoid Square

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**Proving a quadrilateral is a parallelogram you may do any of the following:**

* Prove two pairs of opposite sides parallel * Prove two pairs of opposite sides congruent * Prove one pair of opposite sides both parallel and congruent * Prove the diagonals bisect each other

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Proving a quadrilateral is a rectangle, first prove the figure is a parallelogram and then use one of the following approaches: * Prove two adjacent sides perpendicular * Prove one angle is a right angle * Prove the diagonals are congruent

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Proving a quadrilateral is a rhombus, first prove the figure is a parallelogram and then use one of the following approaches: * Prove one pair of consecutive sides congruent * Prove diagonals bisect the angles * Prove diagonals are perpendicular to each other

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Proving a quadrilateral is a square, first prove the figure is a parallelogram and then use one of the following approaches: * Prove one pair of consecutive sides congruent and at least 1 right angle * Prove diagonals bisect the angles and one pair of consecutive sides is congruent * Prove diagonals are congruent and perpendicular to each other * Prove diagonals are congruent and one pair of consecutive sides congruent

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**Proving a quadrilateral is a trapezoid:**

* Prove only one pair of opposite sides is parallel

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Proving a quadrilateral is an isosceles trapezoid, first prove the figure is a trapezoid and then use one of the following approaches: * Prove the non-parallel sides are congruent * Prove the diagonals are congruent * Prove one pair of base angles are congruent

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**YES YES YES YES NO YES YES YES YES YES YES YES YES NO NO YES YES YES**

Two non-parallel sides are congruent YES YES YES YES NO YES Only Two sides are parallel Two non-congruent sides are parallel YES YES YES YES YES YES YES NO NO YES YES YES YES NO NO YES YES YES YES NO NO NO YES NO YES NO NO

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**NO YES NO YES NO NO NO NO YES YES NO NO NO YES NO YES NO YES NO NO YES**

All angles congruent NO NO All angles congruent NO YES

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