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Math · Grade 3 Math

Chapter 7: Shapes and Problem Solving

The Quadrilateral Family

A square is a rectangle, and both are quadrilaterals.

Lesson
1
Time
About 13 minutes
0 of 7 done

Step 1: Let's Learn

Read it, or press Listen and follow the words.

Any shape with 4 straight sides is a quadrilateral. That is the whole family.

Members of the family

Squares, rectangles, rhombuses, and trapezoids all have 4 sides.

Categories inside categories

A square has 4 square corners, so it is a rectangle. And it has 4 sides, so it is a quadrilateral too.

One shape, several true names

A square can be called a square, a rectangle, and a quadrilateral. All three are correct.

A family, not a list

A quadrilateral is any shape with four straight sides. Rectangles, squares, rhombuses and trapeziums are all quadrilaterals. They are not separate categories sitting side by side — they are members of one family, some of which are also members of each other.

Every square is a rectangle

A rectangle is a quadrilateral with four right angles. A square has four right angles, so it qualifies — it just also happens to have four equal sides. So every square is a rectangle, but not every rectangle is a square. This surprises most people the first time.

Definitions decide, not appearances

Whether a shape belongs to a category is settled by checking the definition, not by whether it looks typical. A very long thin rectangle is still a rectangle. Learning to test against a definition rather than against a mental picture is a real mathematical habit.

Step 2: Try It Yourself

Tap and try it out.

A square: 4 equal sides and 4 square corners.

Square

Straight sides

4

Corners

4

A square has 4 sides that are all the same length.

Turning it does not change what it is.

A rhombus: 4 equal sides, but the corners are not square.

Rhombus

Straight sides

4

Corners

4

A rhombus has 4 sides that are all the same length.

Turning it does not change what it is.

Step 3: Watch an Example

One step at a time.

Watch Ana Name a Shape Three Ways

Ana is shown a square and asked what it is.

  1. Step 1

    She counts 4 equal sides and 4 square corners, so it is a square.

Step 4: Your Turn

Practice makes it stick.

Is It a Quadrilateral?

Problem 1 of 2

Is a trapezoid a quadrilateral?

The Other Way

Problem 2 of 2

Is every rectangle a square?

Naming the Family

1 of 3

How many sides does a quadrilateral have?

2 of 3

Is a square a rectangle?

3 of 3

Is a rhombus a quadrilateral?

Step 5: Quick Check

Show what you know.

Question 1 of 2

How many sides does every quadrilateral have?

Question 2 of 2

Can one shape have more than one correct name?

What You Learned

  • A quadrilateral is any shape with 4 straight sides.
  • Squares, rectangles, rhombuses, and trapezoids are all quadrilaterals.
  • One shape can have several correct names.