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Classifying
Quadrilaterals

Learn to use sides and angles to name four-sided shapes like squares, rectangles, and parallelograms.

ISEE Lower Level

What Is a Quadrilateral?

A quadrilateral is any closed shape with exactly 4 straight sides and 4 corners (called vertices). The word comes from "quad" meaning four.

4 sides 4 corners

Key Words to Know

Parallel
Two sides that are always the same distance apart and never touch, like train tracks.
Right Angle
A square corner that measures exactly \( 90^\circ \), like the corner of a book.
Equal Sides
Sides that have the very same length as each other.

Why Does This Matter?

Knowing the right name for a shape lets you describe its properties without measuring. If you know a shape is a square, you instantly know all 4 sides are equal and all 4 angles are \( 90^\circ \).

all sides equal Square 4 equal sides 4 right angles

The Quadrilateral Family

Many quadrilaterals are special because of their sides and angles. Here are the most important ones to recognize:

Square Rectangle Parallelogram Rhombus Trapezoid

The Parallelogram Rule

A parallelogram is a quadrilateral where both pairs of opposite sides are parallel. Opposite sides are also equal in length.

parallel parallel

Special Parallelograms

Rectangle
4 right angles. Opposite sides equal, but not all sides equal.
Rhombus
All 4 sides equal, but the corners are not necessarily right angles.
Square
All 4 sides equal AND all 4 right angles. The "best of both!"

Trapezoid vs Parallelogram

Trapezoid only 1 parallel pair Parallelogram

How to Classify a Shape

1
Count the sides. Make sure it has exactly 4 to be a quadrilateral.
2
Check for parallel sides. Are there one pair or two pairs?
3
Look at the angles. Are any of them right angles (\( 90^\circ \))?
4
Compare side lengths. Are all sides equal, or just opposite sides?

Worked Example 1

A shape has 4 equal sides and 4 right angles. What is it?

4 equal sides 4 right angles

Worked Example 2

A shape has 4 right angles, but the top and bottom are longer than the sides. What is it?

long top long bottom

Worked Example 3

A shape has only one pair of parallel sides. The other two sides are not parallel. What is it?

parallel parallel

Common Mistakes

✕ All Rectangles are Squares?
Not all rectangles are squares. A square needs equal sides too.
✕ Forgetting angles
A rhombus has equal sides but is NOT a square unless it has right angles.
✕ Counting parallels
A trapezoid has just one parallel pair, not two like a parallelogram.

Quick Summary

Shape Parallel Sides Equal Sides Right Angles
Square2 pairsAll 4Yes
Rectangle2 pairsOppositeYes
Rhombus2 pairsAll 4Not necessarily
Parallelogram2 pairsOppositeNot necessarily
Trapezoid1 pairVariesVaries

Question 1 of 5

Which shape has 4 equal sides and 4 right angles?

Question 2 of 5

A quadrilateral has only one pair of parallel sides. What is it?

Question 3 of 5

The angles of any quadrilateral always add up to which total?

Question 4 of 5

A shape has 4 equal sides but its corners are not right angles. What is it?

Question 5 of 5

Which statement about a rectangle is always true?

Great Work!

You can now classify quadrilaterals by checking sides, parallel pairs, and right angles. Keep practicing and you'll name any shape with confidence!