Geometry and Trigonometry

Plane Geometry

What are the various types of quadrilaterals?

There are several types of quadrilaterals: polygons with four sides. Interestingly enough, some definitions can be “combined”; for example, if a quadrilateral is both a rhombus and a rectangle, it is truly a square. The following lists the common quadrilaterals:

Square—The most obvious quadrilateral is the square. It is an equiangular quadrilateral with four right angles (it is also defined as having four congruent sides).

Rectangle—The second most well-known quadrilateral is the rectangle, a quadrilateral with four right angles, with the opposite sides parallel and congruent, and opposite angles congruent.

Parallelogram—A parallelogram is a quadrilateral with both pairs of opposite sides parallel; thus, opposite sides and angles are congruent.

Rhombus—A rhombus is a parallelogram with four equilateral (or congruent) sides.

Trapezoid—A trapezoid is a quadrilateral with exactly one pair of parallel sides. This is also seen in books as “a quadrilateral with at least one pair of parallel sides,” but this latter definition is often debated among mathematicians, as the meaning is not the same as the first statement. With trapezoids, the parallel sides are called the bases; the nonparallel sides are called the legs.

Isosceles trapezoid—An isosceles trapezoid is one with nonparallel sides that are equal in length, or a trapezoid with a pair of equiangular base angles. The legs of an isosceles trapezoid are congruent. (For more about these figures, see elsewhere in this chapter.)


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