Properties of Quadrilaterals

Quadrilaterals Two-dimensional, closed shape Four straight sides and four angles Sum of angles: 360⁰ Diagonals AC, BD Line segment from one vertex to the opposite vertex Seven types of quadrilaterals

Parallelogram Opposite sides are parallel & equal Opposite angles are equal

Types of Parallelograms Rectangle Square Rhombus Parallelogram All angles are 90⁰ Parallelogram All angles are 90⁰ All sides are equal in length Parallelogram Opposite angles are equal, do not have to be 90⁰ All sides are equal in length

Trapezoid One pair of opposite sides are parallel A “regular” trapezoid: non-parallel sides ARE equal base angles are equal Regular trapezoid

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Other Quadrilaterals Irregular quadrilaterals Kite No specifications Two pairs of adjacent sides are equal in length One pair of opposite angles (the ones that are between the sides of unequal length) are equal in size. One diagonal bisects the other. Diagonals intersect at right angles.

Area of Quadrilaterals Area is measured in square units Number of squares required to cover the surface Be consistent with units Example: If a rectangle is 6 inches wide and 4 feet long, what is the area? Solution: Must convert units to make both measurements consistent. 6 inches = ½ feet ½ ft x 4 ft = 2 ft² Area = 2 ft²

Area of Quadrilaterals Type of Quadrilateral Area Formula Parallelogram A = bh Rectangle Square A = s² Rhombus A = bh or (1/2)d1*d2 Trapezoid A = (1/2)h(b1 + b2) Kite A = (1/2)(d1*d2) Irregular Break into parts & add Key: b – base h – height s – side b1/b2 – base1/base2 d1/d2 – diagonal1/diagonal2