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4th grade

Unit 11: Lesson 5

Classifying geometric shapes

Quadrilaterals review

Review the following quadrilaterals: parallelogram, trapezoid, rhombus, rectangle, and square.  Then, try some practice problems.

Quadrilateral Summary

NameDefinitionExample
Quadrilateral4 sided figure
Parallelogram2 pairs of parallel sides
TrapezoidExactly 1 pair of parallel sides
Rectangle4 right angles
Rhombus4 equal sides
Square4 equal sides and 4 right angles
To learn more about each shape and practice identifying them, keep reading!

What is a quadrilateral?

A quadrilateral is a 4 sided closed figure.
These figures are quadrilaterals:
A shape with four sides. The shape has one set of parallel sides and does not have any right angles.
A shape with four sides. The adjacent sides are of unequal length. The shape has two sets of parallel sides and does not have any right angles.
These figures are NOT quadrilaterals:
An open shape with five sides.
A shape with five sides of equal length.
The start color #e84d39, start text, f, i, r, s, t, end text, end color #e84d39 figure is not closed.
The start color #e07d10, start text, s, e, c, o, n, d, end text, end color #e07d10 figure has 5 sides

Practice set 1: Identifying quadrilaterals

Problem 1A
Which TWO of the following shapes are quadrilaterals?
Choose all answers that apply:
Choose all answers that apply:

Want to learn more about quadrilaterals? Check out these videos:
Types of quadrilaterals
Quadrilateral properties
Classifying quadrilaterals

What is a parallelogram?

A parallelogram is a quadrilateral with 2 pairs of parallel sides. In these figures, sides of the same color are parallel to each other.
A shape with four sides of equal length. The shape has two sets of parallel sides and does not have right angles.
A shape with four sides. The adjacent sides are of unequal length. The shape has two sets of parallel sides and has four right angles.
A shape with four sides of equal length. The shape has two sets of parallel sides and has four right angles.

Practice set 2: Identifying parallelograms

Problem 2A
Which TWO of the following shapes are parallelograms?
Choose all answers that apply:
Choose all answers that apply:

What is a trapezoid?

A trapezoid is a quadrilateral with exactly start color #1fab54, 1, start text, space, p, a, i, r, space, o, f, space, p, a, r, a, l, l, e, l, space, s, i, d, e, s, end text, end color #1fab54.
A shape with four sides. The shape has one set of parallel sides and does not have right angles.
A shape with four sides. The shape has one set of parallel sides and has two right angles.
Problem 3A
Which TWO of the following shapes are trapezoids?
Choose all answers that apply:
Choose all answers that apply:

What is a rectangle?

A rectangle is a quadrilateral with 4 right angles.
A shape with four sides of equal length. The shape has two sets of parallel sides and has four right angles.
A shape with four sides. The adjacent sides are of unequal length. The shape has two sets of parallel sides and has four right angles.
Problem 4A
Which TWO of the following shapes are rectangles?
Choose all answers that apply:
Choose all answers that apply:

What is a rhombus?

A rhombus is a quadrilateral with 4 equal sides.
A shape with four sides of equal length. The shape has two sets of parallel sides and does not have right angles.
A shape with four sides of equal length. The shape has two sets of parallel sides and has four right angles.
Problem 5A
Which TWO of the following shapes are rhombuses?
Choose all answers that apply:
Choose all answers that apply:

What is a square?

A square is a quadrilateral with 4 equal sides and 4 right angles.
A shape with four sides of equal length. The shape has two sets of parallel sides and has four right angles.
A shape with four sides of equal length. The shape has two sets of parallel sides and has four right angles.
Problem 6A
Which TWO of the following shapes are squares?
Choose all answers that apply:
Choose all answers that apply:

Practice set 7: Pulling it all together

Problem 7A
All parallelograms have opposite sides that are equal in length and parallel.
Which of these quadrilaterals are parallelograms?
The matching arrow labels indicate that two opposite sides are parallel.

Parallelogram
Not parallelogram

Want to try more problems like this? Check out these exercises:
Identify quadrilaterals
Quadrilateral types
Categorize quadrilaterals

Want to join the conversation?

• why can a square be a rectangle but a rectangle can not be a square.
(2 votes)
• So a square is a special kind of rectangle, it is one where all the sides have the same length. Thus every square is a rectangle because it is a quadrilateral with all four angles right angles. However not every rectangle is a square, to be a square its sides must have the same length.
(26 votes)
• is there a way that a rectangle can be a square without cutting it
(6 votes)
• yes, well technically a square is a type of rectangle
(8 votes)
• What does perpendicular mean?
(11 votes)
• it is two lines that intersect but make right angles
(2 votes)
• how can a square be a rectangle it is just a square in't it
(8 votes)
• A rectangle is just a shape that has four right (90 degree) angles and four sides where opposite sides are parallel. There’s also a special type of rectangle that also has all of the sides be the same length. We call that special type of rectangle a “square”.

I hope this helps!
(2 votes)
• Hi
Why can a square be a rectangle but a rectangle can’t be a square
(8 votes)
• Hi the reason why a rectangle cant be a square is that a square has 4 sides and 4 right angles and NEEDS to have equal sides and a rectangle can have 4 sides 4 right angles and doesnt need to have equal sides i hope this helps
(1 vote)
• Why do the shapes have the same sides but mean different things
(7 votes)
• So a square is a special kind of rectangle, it is one where all the sides have the same length. Thus every square is a rectangle because it is a quadrilateral with all four angles right angles. However not every rectangle is a square, to be a square its sides must have the same length.
(7 votes)
• how is a rectangle a square and a square a rectangle i dont understand.
(6 votes)
• RIGHT I also got confused about that =
(3 votes)
• it seems that a rhombus cannot be a rectangle without being a square is that true?
(5 votes)
• Yes, you are correct. Good job!
(5 votes)
• for all the people wondering for a square to be a rectangle it has to be because a rectangle needs to have 4 right angles which a square has but a square needs equal sides and 4 right angles wich a rectangl does not have
(7 votes)