The Basics of Quadrilaterals Study Guide

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Updated on Oct 3, 2011

Introduction to The Basics of Quadrilaterals

Do not worry about your difficulties in mathematics, I assure you that mine are greater.

—Albert Einstein (1879–1955)

In this lesson, you will learn about a shape called a quadrilateral, which is famous for having four sides. Quadrior quattor means "four" in Latin, and lateral means "side," so when we say a shape is a quadrilateral, we mean it has four sides. A quadrilateral can be further classified into many different forms, but here we will focus on the most important family of quadrilaterals—trapezoids and parallelograms, along with their sub-shapes.

A Quadrilateral isa two-dimensional closed shape with four sides. A line drawn from one vertex of a quadrilateral to the opposite vertex is called a diagonal.

Types of Quadrilaterals

A quadrilateral with one pair of parallel sides (bases) is called a trapezoid. In an isosceles trapezoid, the sides that are not bases are congruent. Because the parallel bases are not the same length in a trapezoid, we call these bases b1 and b2. Trapezoids have exactly one pair of parallel sides.


Parallelograms have two pairs of parallel sides. The opposite sides are congruent. The opposite angles are congruent. The diagonals of parallelograms bisect each other.


Parallelograms are broken down into further subgroups.

Rectangles are parallelograms with four right angles. This means that the diagonals of a rectangle bisect each other.


A rhombus is a parallelogram with four congruent sides. The diagonals of a rhombus bisect not only each other, but also the angles that they connect! Also, the diagonals are perpendicular.


A square is a rhombus with four right angles.


Find practice problems and solutions for these concepts at The Basics of Quadrilaterals Practice Questions.

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