Special Quadrilateral Definitions and Properities

Parallelogram

A quadrilateral with both pairs of opposite sides parallel

Parallelogram Property 1

Opposite sides are congruent (P)

Parallelogram Property 2

Opposite angles are congruent (P)

Parallelogram Property 3

Diagonals bisect each other (P)

Parallelogram Property 4

Consecutive angles are supplementary (P)

Rhombus

Parallelogram with at least two consecutive sides are congruent

Rhombus Property 1

All properties of a parallelogram (R)

Rhombus Property 2

All sides are congruent (R)

Rhombus Property 3

Diagonals bisect the angles (R)

Rhombus Property 4

Diagonals are perpendicular bisectors of each other (R)

Rectangle

Parallelogram with at least one right angle

Rectangle Property 1

All properties of a parallelogram (rectangle)

Rectangle Property 2

All angles are right angles (rectangle)

Rectangle Property 3

Diagonals are congruent (rectangle)

Square

Parallelogram that is both a rhombus and a rectangle

Square Property 1

All properties of a parallelogram (S)

Square Property 2

All properties of a rhombus (S)

Square Property 3

All properties of a rectangle (S)

Kite

A quadrilateral with 2 pairs of consecutive sides congruent, but opposite sides are not congruent

Kite Property 1

Diagonals are perpendicular (K)

Kite Property 2

ONE diagonal is the perpendicular bisector of the other (K)

Kite Property 3

ONE diagonal bisects a pair of opposite angles (K)

Kite Property 4

ONE pair of opposite angles are congruent

Trapezoid

A quadrilateral with exactly one pair of parallel sides

Trapezoid Property 1

Bases are parallel (T)

Trapezoid Property 2

Some consecutive angles are supplementary (T)

Isosceles Trapezoid

A trapezoid in which the non-parallel sides (legs) are congruent

Isos. Trapezoid Property 1

All properties of a trapezoid (IT)

Isos. Trapezoid Property 2

Lower base angles are congruent (IT)

Isos. Trapezoid Property 3

Upper base angles are congruent (IT)

Isos. Trapezoid Property 4

Diagonals are congruent (IT)