CLASSIFYING QUADRILATERALS
TERMINAL OBJECTIVE: Be able to correctly classify a quadrilateral as
a trapezoid, parallelogram, rectangle, rhombus, or square if possible.
Unlike some parts of algebra, geometry is all around and is very real. Quadrilaterals are
often used in construction of buildings and in decorative patterns. Below are a few examples of
where quadrilaterals can be found.
Knowing how to classify quadrilaterals will
help you better understand the properties of
each type of quadrilateral.
You will work through each lesson individually and complete the questions associated
with each lesson. Answers are provided to the questions from each lesson provided at the end of
this packet. Use the answers as a way of checking your understanding as you work through each
lesson. At the end of the lessons you will take a post test to determine if you learned how to
classify quadrilaterals. Remember, your posttest will be scored and is worth 100 points.
1
LESSON 1
Objective: Given a set of figures, correctly identify which figures are polygons.
A polygon is a closed plane figure formed by three or more segments.
The following are polygons:
The following are not polygons:
B.
D.
A.
These are all polygons because they are
closed plane figures formed by segments.
C.
A, C, and D are not polygons because they are
formed by curves and not segments.
B is not a polygon because it is not a closed
figure.
Activities and Practice Items:
1) Circle all of the figures that are polygons.
A.
B.
C.
D.
E.
2
LESSON 2
Objective: Given a set of polygons, correctly identify which figures are quadrilaterals.
A quadrilateral is a four sided polygon.
The following are quadrilaterals:
The following are not quadrilaterals:
These are not quadrilaterals because they do not
have four sides.
Activities and Practice Items:
1) Circle all of the figures that are quadrilaterals.
A.
B.
C.
D.
E.
3
LESSON 3
Objective: Identify the characteristics of a quadrilateral.
In order to classify a quadrilateral you need to identify certain characteristics of the quadrilateral.
These characteristics include having right angles, parallel sides and congruent segments.
Part 1
To identify parallel sides you can look for parallel markings. Remember, parallel lines are
marked with arrows. If no parallel markings are given you can still identify parallel lines by
extending them to confirm that they will never intersect. All of the quadrilaterals below have
parallel lines.
S
A
T
R
B
D
U
C
One pair of
Two pair of
Two pair of
parallel sides
parallel sides
parallel sides
Deciding if a quadrilateral has one, two or no pairs of parallel sides is the first step to classifying
quadrilaterals. In this lesson you will identify parallel lines by coloring over the lines that are
parallel with the same color. For example,
The red lines are parallel to
Only the green lines are
each other and the blue lines
parallel to each other.
are parallel to each other.
Activities and Practice Items:
1) For each figure, color the lines that are parallel the same color.
A.
B.
2) How many pairs of parallel sides does each figure have? One pair, two pairs or no pairs of
parallel sides?
B
A
B
A
D
C
D
A
B
G
H
C
C
D
F
E
4
Part 2:
To identify right angles you can use a protractor to confirm that the measure is 90° or you can
look for the box in the corner. This box represents 90°. All of the quadrilaterals below have
right angles.
This quadrilateral has two right angles
Both of these quadrilaterals have four
that are marked with a box in the
right angles. This can be confirmed by
corner.
measuring them with a protractor.
When classifying quadrilaterals it is important to recognize when a figure has four right angles.
In this lesson you will be asked to circle the quadrilaterals that have four right angles.
For example,
This quadrilateral has two right angles
that are marked with a box in the
corner.
Activities and Practice Items:
3) Circle all of the quadrilaterals that have four right angles.
A.
B.
C.
D.
5
Part 3:
To identify congruent segments you can look for congruent markings or you can use a ruler.
Remember, congruent means that the segments have the same length. All of the quadrilaterals
below have congruent sides.
B
7cm
10cm
C
C
D
A
8 m
3 m
3 m
1 0 cm
D
A
7cm
D
A
B
C
8 m
B
Activities and Practice Items:
4) Mark all congruent sides with congruent tick marks.
A.
B.
C.
6
Part 4:
5) Place an “X” in the cell beneath each characteristic that the quadrilateral has.
Quadrilateral
No parallel
sides
Only one pair
of parallel sides
Two pairs of
parallel sides
Four right
angles
Four congruent
sides
Four right angles and
four congruent sides
7
LESSON 4
Objective: Using the number of pairs of parallel sides a quadrilateral has, classify the
quadrilateral as a trapezoid, parallelogram or simply a quadrilateral.
Quadrilaterals can be classified based on how many pairs of parallel sides it has.
Only one pair of parallel sides → classify as a TRAPEZOID
Two pairs of parallel sides → classify as a PARALLELOGRAM
No parallel sides → QUADRILATERAL
(A four sided figure that has no parallel sides can only be classified as a quadrilateral.)
One pair of parallel
sides → trapezoid
Two pairs of parallel
sides → parallelogram
No pairs of parallel sides → can only
be classified as a quadrilateral
Activities and Practice Items:
1) Based on whether the quadrilateral has one, two or no parallel sides classify each
quadrilateral below as a trapezoid, parallelogram, or simply a quadrilateral.
A.
B.
C.
8
LESSON 5
Objective: Based on whether a quadrilateral has four right angles, four congruent sides or
both, classify the quadrilateral as a rectangle, square, or rhombus.
Quadrilaterals can be classified based on whether or not they have four right angles, four
congruent sides or both four right angles and four congruent sides.
Four right angles → RECTANGLE
Four congruent sides → RHOMBUS
Both four right angles and four congruent sides → SQUARE
Four right angles → rectangle
Four congruent
sides→ rhombus
C
D
A
B
Four congruent sides and four
right angles→ rhombus
Activities and Practice Items:
1) Classify each quadrilateral below as a rectangle, rhombus, or square.
A.
B.
C.
9
LESSON 6
Terminal Objective: Correctly classify a quadrilateral as a trapezoid, parallelogram,
rectangle, rhombus, or square if possible.
Quadrilaterals are classified by their characteristics. Quadrilaterals can be classified as more
than one type of quadrilateral. Use the diagram below to determine how many ways a given
quadrilateral can be classified.
QUADRILATERAL
A polygon with
four sides.
PARALLELOGRAM
TRAPEZOID
Two pairs of
parallel sides.
Only one pair of
parallel sides.
RHOMBUS
RECTANGLE
Four congruent
sides.
Four right angles.
SQUARE
Four right angles
and four congruent
sides
A square can be classified as
everything above it: a rectangle, a
rhombus, a parallelogram and a
quadrilateral.
10
Activities and Practice Items:
1) Use as many names a possible to classify each quadrilateral. Circle the name that is most
specific.
A.
B.
C.
2) Determine if each statement is true or false. Explain.
a) All squares are rectangles.
b) All trapezoids are parallelograms.
c) A rhombuses are squares.
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POST TEST
1. Is the figure below a polygon? Why or why not?
2. Circle the polygons that are quadrilaterals:
3. Draw a box in the corner of all of the right angles.
G
H
F
E
B
C
A
D
4. For each figure, color each pair of parallel sides the same color.
S
R
A
T
U
B
D
C
5. Mark all congruent sides with congruent tick marks
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6. How many pairs of parallel sides does the figure below have? One pair, two pairs or no pairs
of parallel sides?
A
B
D
C
7. What is the most specific name for the figure below?
8. What is most specific name for the figure below?
9. What is most specific name for the figure below?
10. Circle the parallelograms below that have four right angles. You may use a protractor to
measure the angles.
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11. Circle the parallelograms below that have four congruent sides. You may use a ruler to
measure the side lengths.
12. What is most specific name for the figure below?
13. What is most specific name for the figure below?
14. What is most specific name for the figure below?
15. Use as many names a possible to classify the quadrilateral. Circle the name that is most
specific.
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