QuadrilateralsMA1G3d. Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.

Quadrilaterals are simply four-sided shapes. The lines have to be straight, and the shape has to be two-dimensional, but that is all that’s necessary to make it a quadrilateral.

General Properties: Four sides (edges) Four corners (vertices) Interior angles add up to 360 degrees

Special Quadrilaterals

Rectangle Four-sided shape with four right (90-

degree) angles. Opposite sides are parallel and of equal

length

Special Quadrilaterals Rhombus

Four-sided shape where all sides are of equal length.

Opposite sides are parallel Opposite angles are equal Diagonals (dashed lines in second figure) of a

rhombus bisect each other at right angles.

Special Quadrilaterals Square

All sides are equal, and every angle is 90-degrees. Opposite sides are parallel Fits definition for both rectangle and rhombus

Special Quadrilaterals Parallelogram

Opposite sides are parallel and equal in length Opposite angles are equal (angles "a" are the same,

and angles "b" are the same)

Special Quadrilaterals Trapezoid

One pair of opposite sides are parallel It is called an Isosceles trapezoid if the sides that

aren't parallel are equal in length and both angles coming from a parallel side are equal, as shown.

Special Quadrilaterals Kite

Hey, it looks like a kite. It has two pairs of sides. Each pair is made up of adjacent sides that are equal in length. The angles are equal where the pairs meet. Diagonals (dashed lines) meet at a right angle, and one of the diagonal bisects (cuts equally in half) the other.