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Geometry for Kids6 chapters | 45 lessons

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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!

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.

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.

The green shape is a parallelogram, which is a trapezoid with two pairs of parallel sides. That is a tongue twister!

The purple shape is a rhombus, which has two pairs of parallel sides, just like a parallelogram. In addition, all four of its sides are congruent.

The red shape is a rectangle, which is a parallelogram with four right angles.

The orange shape is a square, which is a rhombus and rectangle with four congruent sides and four right angles.

Let's think about a square for a moment. When you think about a square, you probably think about the shape with four congruent sides and four right angles. That is true! But, what if I told you that the shape you were thinking of is also a rectangle? And also a parallelogram, rhombus, trapezoid, kite, and quadrangle? Say, what? Yes, it's true!

Do you see how all arrows make a path eventually to reach the square? That is because a square is basically a very specific type of quadrangle, kite, trapezoid, rhombus, parallelogram, and rectangle. Wow! A square is any one of those 6 other shapes that has four right angles and four congruent sides. How neat!

A **quadrangle** is a shape with four angles. All quadrangles are **quadrilaterals**. There are six different types of quadrangles: **trapezoid, kite, parallelogram, rhombus, rectangle**, and **square**.

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Geometry for Kids6 chapters | 45 lessons

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