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Classify quadrilaterals, including rectangles, rhombuses, and squares.

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?

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?

Challenge problem

Let's consider one more shape:

Does the shape have four right angles?

So, is the shape a rectangle?

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:

Try it yourself

Which of the following shapes are rhombuses?

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?

Challenge question 1

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

Challenge question 2

Which of the following describe this shape?

Want to join the conversation?

• Why is a square a rectangle?
• A rectangle is a specific type of quadrilateral, and a square is a specific type of rectangle so you can think of a square as a subset of a subset, also you can think of a square as a rectangle and a rhombus combined
• Why is a square a special shape?
• A square is the type of quadrilateral (four-sided figure) with the most properties. A square has four equal sides and four right (90-degree) angles. These two properties lead to more properties.

A square’s two diagonals are equal in length.

A square’s two diagonals form a right (90-degree) angle at the point where they cross each other.

A square’s two diagonals divide each other into two equal segments.

A square’s two diagonals divide each of the square’s four right (90-degree) angles into two equal 45-degree angles.

Opposite sides of a square are parallel.

A square has the most lines of symmetry (four), of all quadrilaterals.

Have a blessed, wonderful day!
• Is a heart a type of circle?
• No.
A circle has 1 side and infinite lines of symmetry.
A heart doesn't have either of those.
• How many shapes are there in the world?
• I would have to guess that the number of shapes in the world cannot be counted accurately because there are so many.

I'm not suggesting that you do it, but imagine cutting down EVERY tree in the world. You would find that every tree trunk has a different shape than all the others. Every snow flake apparently is a different shape than all the others. Every cloud has a different shape, every leaf has a different shape, every stream has a different shape. Etc.

There are just too many to count.
• Is there a group for things without paralel sides. I hope there is. and if there isn't a group that is pure weird because every quadrilateral should have a group. The square is so lucky because it is every group
• Those are mostly classified by the number of sides they have so if you had a 4 sided shape with no parallel sides it's just called a quadrilateral.
• How are rectangles and squares the same thing if they don’t look the same?
• Let’s look at the definitions of a rectangle and a square.

A rectangle is a quadrilateral (four-sided polygon) with four right angles.

A square is a quadrilateral with four right angles and four equal sides.

These definitions tell us that a square is a special type of rectangle. So all squares are rectangles. However, only some rectangles are squares. Rectangles with unequal length and width are not squares. Rectangles with equal length and width are also squares.
• Is a square in every category of quadrilaterals?
• Is a rectangle a parallelogram?
• Good question!

A rectangle is defined as a quadrilateral with four right angles.

A parallelogram is defined as a quadrilateral with two pairs of parallel sides.

In a rectangle, any two sides next to each other are perpendicular. So any two opposite sides are perpendicular to a third side, and therefore are parallel to each other. Therefore, a rectangle also has two pairs of parallel sides. This means that all rectangles are parallelograms.

However, not all parallelograms are rectangles (for example, think of a quadrilateral with two parallel horizontal sides and two parallel diagonal sides).