What is a Quadrangle? - Definition & Shapes

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  • 0:03 Definition of a Quadrangle
  • 1:11 The Quadrangle Family Tree
  • 2:18 What Is a Square?
  • 3:01 Lesson Summary
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Lesson Transcript
Instructor: Allison Petrovic

Allison has experience teaching high school and college mathematics and has a master's degree in mathematics education.

Did you know that a square can also be classified as a rectangle, and even a quadrangle? What is a quadrangle? You will find out in this fascinating lesson!

Definition of a Quadrangle

To best understand the definition of quadrangle, let's look at the prefix and base word. The prefix of our word is 'quad-' and the base word is 'angle.' Another word for quad is four. So a quadrangle is a shape with four angles. All shapes that have four angles also have four sides. So, all quadrangles are quadrilaterals.

The short definition for a quadrilateral is a shape with four sides! This is the short definition since there are a few details that each shape must have in order to be classified as a quadrangle, or, as it is more frequently called, quadrilateral. To be considered a quadrilateral, the shape must:

  • Have four straight sides
  • Be a flat shape (meaning 2-dimensional)
  • Be a closed figure

Take a look at this picture, and let's identify whether each figure is a quadrilateral or not:


The green shape is a quadrilateral since it has four straight sides all of which are in the same dimension, and all sides are connected. The purple shape is not a quadrilateral because it only has 3 sides. The red shape is not a quadrilateral since all sides do not meet: you can see a gap at one corner.

The Quadrangle Family Tree

Let's take a look at another picture. This one shows 6 examples of quadrangles. Remember, these are all types of quadrangles. So, a trapezoid, kite, parallelogram, rhombus, rectangle, and square are all types of quadrilaterals.



The gray shape is a trapezoid, which is a quadrangle with at least one pair of parallel sides. Parallel lines are lines that are the same distance apart and will never meet. I like to think of a trapezoid as the bottom piece of a triangle if you were to rip it in half horizontally.


The blue shape is a kite, which is a quadrangle with two pairs of congruent sides. Congruent means having the same length. A kite looks like a diamond.

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