 Presentation on theme: "Quadrilateral Proofs."— Presentation transcript:

Parallelogram Trapezoid Rectangle Rhombus Isosceles Trapezoid Square

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

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

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

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

Proving a quadrilateral is a trapezoid:
* Prove only one pair of opposite sides is parallel

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

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

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