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Course: 5th grade (Eureka Math/EngageNY)>Unit 5

Lesson 4: Topic D: Drawing, analysis, and classification of two-dimensional shapes

Quadrilaterals review

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

Quadrilateral Summary

NameDefinitionExample
Quadrilateral$4$ sided figure
Parallelogram$2$ pairs of parallel sides
TrapezoidExactly $1$ pair of parallel sides
Rectangle$4$ right angles
Rhombus$4$ equal sides
Square$4$ 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:
These figures are NOT quadrilaterals:
The $\text{first}$ figure is not closed.
The $\text{second}$ figure has $5$ sides

Practice set 1: Identifying quadrilaterals

Problem 1A
Which TWO of the following shapes are quadrilaterals?
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.

Practice set 2: Identifying parallelograms

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

What is a trapezoid?

A trapezoid is a quadrilateral with exactly .
Problem 3A
Which TWO of the following shapes are trapezoids?
Choose all answers that apply:

What is a rectangle?

A rectangle is a quadrilateral with $4$ right angles.
Problem 4A
Which TWO of the following shapes are rectangles?
Choose all answers that apply:

What is a rhombus?

A rhombus is a quadrilateral with $4$ equal sides.
Problem 5A
Which TWO of the following shapes are rhombuses?
Choose all answers that apply:

What is a square?

A square is a quadrilateral with $4$ equal sides and $4$ right angles.
Problem 6A
Which TWO of the following shapes are squares?
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.

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.
(130 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.
(85 votes)
• is there a way that a rectangle can be a square without cutting it
(7 votes)
• yes, well technically a square is a type of rectangle
(29 votes)
• how can a square be a rectangle it is just a square in't it
(4 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!
(34 votes)
• it seems that a rhombus cannot be a rectangle without being a square is that true?
(16 votes)
• Yes, you are correct. Good job!
(12 votes)
• Hi
Why can a square be a rectangle but a rectangle can’t be a square
(15 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
(6 votes)
• why can a square be a rectangle but a rectangle cant be a square?
(9 votes)
• Because squares have 4 sides like a rectangle but squares have 4 EQUAL sides. Rectangles have 2 pairs of parallel sides.
(5 votes)
• if a square is a rhombus , then why can't a rhombus be a square, they look the same.
(9 votes)
• Because some one sat on it and ruind the anguls
(4 votes)
• Why do the shapes have the same sides but mean different things
(10 votes)
• Im not sure I thought they were all only called congruent
(0 votes)
• what if a parallelogram is not having parallel 2 sides but only one side parallel then which shape would it be?
(3 votes)
• A quadrilateral with 1 side parallel is called a trapezoid
(1 vote)
• i dont know why but every time i put in a awnser for the coordinate part of geometry it says i got it wrong but idk whats happening
(4 votes)