Quadrilaterals Four sided polygons Non-examples Examples

Specific Kinds of Quadrilaterals Parallelogram Rectangle Square Rhombus Trapezoid Kite

Parallelogram Both pairs of opposite sides are parallel. Both pairs of opposite sides are congruent. Both pairs of opposite angles are congruent. Diagonals bisect each other. A B D C

Rectangle Opposite sides are congruent and parallel. Opposite angles are congruent. Consecutive angles are supplementary. Diagonals are congruent and bisect each other. All four angles are right angles. E F G H

Rhombus All sides are congruent. Opposite sides are parallel. J K L All sides are congruent. Opposite sides are parallel. Diagonals are perpendicular and bisect each other . Diagonals are angle bisectors.

Square All sides are congruent. Opposite sides are parallel. All angles are right angles. Diagonals are congruent, perpendicular and bisect each other . Diagonals are angle bisectors. M N O P

Trapezoid Exactly one pair of parallel sides (bases). leg Exactly one pair of parallel sides (bases). Exactly one pair of nonparallel sides (legs).

Isosceles Trapezoid base The legs are congruent. Base angle T R J K The legs are congruent. Both pairs of base angles are congruent. The diagonals are congruent. The median (JK) joins the midpoints of the legs. leg A

Formula to Find the Median of an Isosceles Trapezoid (base + base) 2 = Median D A B C M N 3x-1 10 7x+1 Example: 10x = 10 2 AB + CD = MN 2 2( ) = (10)2 10x 3x – 1 +7x +1 2 = 10 10x = 20 2 10x = 20 10 10 X = 2

Kite Two pairs of adjacent sides are congruent. No opposite sides are congruent. Diagonals are perpendicular.