Classifying Quadrilaterals

“…geometric shapes are the alphabet in which the book of nature is written." -Galileo

What is a Quadrilateral?

A quadrilateral is a two-dimensional figure formed by connecting four segments endpoint to endpoint with each segment intersecting exactly two others. It also has four sides and four angles.

What is a Quadrilateral?

Look around you, do you see shapes that could be termed a quadrilateral?

Take about two minutes to draw five different shapes that you think could be classified as a quadrilateral.

Types of Quadrilaterals

Trapezoid Parallelogram Square Rectangle Kite, Dart Rhombus Rectangle

Copyright © 2000 by Monica Yuskaitis

Quadrilateral Family

parallelogram

rectangle

rhombus square

trapezoid

Classification of Quadrilaterals

A concave quadrilateral contains at least one angle that is >180o.

A quadrilateral is convex if each vertex lies in the interior of the opposite angle.

Name that Quadrilateral!

A square is a quadrilateral with all sides and angles equal.

If all quadrilaterals have 360o total, what is the angle of each vertex in a square?

Name that Quadrilateral!

A quadrilateral with all angles equal is a rectangle.

A quadrilateral with all sides equal is a rhombus.

A quadrilateral with at least one pair of parallel sides is a trapezoid.

Name that Quadrilateral!

Name that Quadrilateral!

A quadrilateral with both pairs of opposite sides parallel and equal in length is known as a parallelogram.

Parallelograms can be considered special cases of trapezoids, since they have a least one pair of parallel sides.

Name that Quadrilateral!

A quadrilateral with two separate pairs of equal adjacent sides is commonly called a kite.

However, if the kite is concave, a dart is a more appropriate term.

Examples of shapes or curves that are not classified as quadrilaterals. They do not follow the definition of a quadrilateral. Can you give a reason why?

Are They Quadrilaterals?

ACB