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Updated on Oct 5, 2011

### Lesson Summary

In this lesson, you will learn how to name and classify special quadrilaterals. You will also learn how to use the special properties associated with parallelograms, rectangles, rhombuses, squares, and trapezoids.

Quadrilaterals are one of the most commonly used figures in buildings, architecture, and design. The diagram on the next page shows the characteristics and relationships among the special quadrilaterals.

All four-sided polygons are classified as quadrilaterals. Quadrilaterals branch off into two distinctive subgroups: parallelograms and trapezoids. Trapezoids are quadrilaterals that have only one pair of opposite parallel sides. If the trapezoid has congruent legs, then the figure is an isosceles trapezoid. The diagram on page 88 shows that an isosceles trapezoid is one type of trapezoid, which is one type of quadrilateral. In other words, the figures become more specialized as the chart flows downward.

The other main branch of quadrilaterals consists of parallelograms. Parallelograms have two pairs of opposite parallel sides. Parallelograms branch off into two special categories: rectangles and rhombuses. A rectangle is a parallelogram with four congruent angles. A rhombus is a parallelogram with four congruent sides. A square is a parallelogram with four congruent angles and four congruent sides. In other words, a square is also a rectangle and a rhombus.

## Properties of Parallelograms

The following properties of parallelograms will help you determine if a figure is a parallelogram or just a quadrilateral. The properties are also useful to determine measurements of angles, sides, and diagonals of parallelograms.

Note that diagonals of a parallelogram are not necessarily congruent. Watch out for this, because it is a common error.

#### Examples:

BMAH is a parallelogram.

## Other Special Properties of Quadrilaterals

The rectangle, rhombus, and square have a few other special properties. First, remember that these figures are all parallelograms; therefore, they possess the same properties as any parallelogram. However, because these figures are special parallelograms, they also have additional properties. Since a square is both a rectangle and a rhombus, a square possesses these same special properties.

Practice problems for these concepts can be found at: Quadrilaterals Practice Questions.

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