Classify quadrilaterals, including rectangles, rhombuses, and squares. 

Quadrilaterals

A quadrilateral is a polygon with four sides.

Study some examples

Here are some examples of quadrilaterals:

Try it yourself

Which of the following shapes are quadrilaterals?
Choose all answers that apply:
Choose all answers that apply:

The following shapes are quadrilaterals because they are polygons with four sides. Remember: polygons must be closed figures.

Special types of quadrilaterals

Some quadrilaterals go by special names like rectangle, rhombus, and square. Let's learn about them!

Rectangles

What makes a shape a rectangle?
  • There are four right angles.
  • There are four sides because it's a quadrilateral.

Study some examples

Here are some examples of rectangles:

Try it yourself

Which of the following shapes are rectangles?
Choose all answers that apply:
Choose all answers that apply:

The following shapes are rectangles because they are quadrilaterals with four right angles. Remember: quadrilaterals must have four sides.*

Challenge problem

Let's consider one more shape:
Is this shape a quadrilateral?
Choose 1 answer:
Choose 1 answer:

Does the shape have four right angles?
Choose 1 answer:
Choose 1 answer:

So, is the shape a rectangle?
Choose 1 answer:
Choose 1 answer:

That's right!
A rectangle is a quadrilateral with four right angles.
Squares are quadrilaterals. Squares have four right angles.
So, squares are rectangles!

Rhombuses

What makes a shape a rhombus?
  • All sides are the same length.
  • There are four sides because it is a quadrilateral.

Study some examples

Here are some examples of rhombuses:
Yes, it is!
A rhombus is a quadrilateral with all sides of equal length.
Squares are quadrilaterals. Squares have all sides of equal length.
So, squares are rhombuses!

Try it yourself

Which of the following shapes are rhombuses?
Choose all answers that apply:
Choose all answers that apply:

The following shapes are rhombuses because they are quadrilaterals with all sides of equal length:

Squares

What makes a shape a square?
  • All sides are of equal length.
  • There are four right angles.
  • There are four sides because it's a quadrilateral.

Study some examples

Here are some examples of squares:

Try it yourself

Which of the following shapes are squares?
Choose all answers that apply:
Choose all answers that apply:

The following shapes are squares because they are quadrilaterals with four right angles and all sides of equal length:

Challenge question 1

Drag the points to create a shape that is both a rectangle and a rhombus.

A start color blueD, r, e, c, t, a, n, g, l, e, end color blueD is a quadrilateral with start color blueD, f, o, u, r, space, r, i, g, h, t, space, a, n, g, l, e, s, end color blueD.
A start color greenD, r, h, o, m, b, u, s, end color greenD is a quadrilateral with start color greenD, a, l, l, space, s, i, d, e, s, space, o, f, space, e, q, u, a, l, space, l, e, n, g, t, h, end color greenD.
A square is a quadrilateral with start color blueD, f, o, u, r, space, r, i, g, h, t, space, a, n, g, l, e, s, end color blueD and start color greenD, a, l, l, space, s, i, d, e, s, space, o, f, space, e, q, u, a, l, space, l, e, n, g, t, h, end color greenD.
So, a square is a start color blueD, r, e, c, t, a, n, g, l, e, end color blueD and a start color greenD, r, h, o, m, b, u, s, end color greenD.
The solution is to draw a square.

Challenge question 2

Which of the following describe this shape?
Choose all answers that apply:
Choose all answers that apply:

A quadrilateral is a four-sided polygon. Is this shape a four-sided polygon? Yes!
A rectangle is a quadrilateral with four right angles. Does this shape have four right angles? Yes!
A rhombus is a quadrilateral with all sides of equal length. Does this shape have all sides of equal length? Yes!
A square is a four-sided polygon with four right angles and all sides of equal length. Is this shape a square? Yes!
So, the shape is a quadrilateral, rectangle, rhombus, and square!