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pat5018  on May 25, 2010

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 If one pair of sides of a quadrilateral are both parallel and congruent......then the quadrilateral is a parallelogram.
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#### Definitions

If one pair of sides of a quadrilateral are both parallel and congruent... ...then the quadrilateral is a parallelogram.
If the diagonals of a parallelogram are congruent... ...then the parallelogram is a rectangle.
If one angle of a parallelogram measures 90 degrees... ...then the parallelogram is a rectangle.
If two adjacent sides of a parallelogram are congruent... ...then the parallelogram is a rhombus.
If the diagonals of a parallelogram are perpendicular... ...then the parallelogram is a rhombus.
parallelogram A quadrilateral with two pairs of parallel, congruent sides.
rhombus A quadrilateral with four congruent sides.
rectangle A quadrilateral with four right angles.
square A quadrilateral with four congruent sides and four right angles.
indirect proof A proof by contradiction. A proof in which the statement you want to prove is assumed to be false.
How does one proceed in an indirect proof? a) Propose a new conditional by negating the original conclusion. b) Show the absurdity of the new conditional.

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