Lesson 11.3
Name
Quadrilaterals
Learning Objective You will describe and
classify each type of quadrilateral and use a
Venn diagram to sort quadrilaterals to find how
they are related.
Essential Question How can you classify and compare quadrilaterals?
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Unlock the
the Problem
Problem
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A seating chart for a baseball field has many four-sided figures,
or quadrilaterals. What types of quadrilaterals can you find in
the seating chart?
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There are five special types of quadrilaterals. You can
classify quadrilaterals by their properties, such as parallel
sides and perpendicular sides. Parallel lines are lines that
are always the same distance apart. Perpendicular lines
are lines that intersect to form four right angles.
Complete the sentence that describes each
type of quadrilateral.
A general quadrilateral has
4 sides and 4 angles.
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▲ Lower Level
A trapezoid is a
quadrilateral with at least
1 pair of __
sides.
A parallelogram is a
special trapezoid with
opposite __
parallelogram with _
right angles and 4 pairs of
that are __
and parallel.
___ sides.
A rhombus is a special
A square is a special
parallelogram with
parallelogram with _
congruent sides.
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A rectangle is a special
_ congruent sides
and _ right angles.
So, the types of quadrilaterals you can find in the seating chart of the field are
_____________.
Math
Talk
Math Processes and Practices 7
Identify Relationships How
are trapezoids and
parallelograms different?
Chapter 11 649
Hands
On
Activity
Materials ■ quadrilaterals ■ scissors
ou can use a Venn diagram to sort quadrilaterals and find out Y
how they are related.
• Draw the diagram below on your MathBoard.
• Cut out the quadrilaterals and sort them into the Venn diagram.
•R
ecord your work by drawing each figure you have placed in
the Venn diagram below.
QUADRILATERALS
QUADRILATERALS
Trapezoids
Trapezoids
Parallelograms
Parallelograms
Rhombuses
Rectangles
Rhombuses
Rectangles
Complete the sentences by writing always,
sometimes, or never.
A rhombus is __ a square.
A parallelogram is __
a rectangle.
A rhombus is __
a parallelogram.
A trapezoid is __
a parallelogram.
A parellelogram is __ a trapezoid.
Squares
A square is __ a rhombus.
Squares
2. E
xplain why the section of the Venn diagram for squares intersects with both
the section for rhombuses and the section for rectangles.
650
© Houghton Mifflin Harcourt Publishing Company
1. Explain why the circle for parallelograms is inside the circle for trapezoids.
Name
Share
Share and
and Show
Show
MATH
BOARD
1. Use quadrilateral ABCD to answer each question. Complete the sentence.
A
B
a.Measure the sides. Are any of the sides congruent? _
Mark any congruent sides.
D
b. How many right angles, if any, does the quadrilateral have? _
C
c. How many pairs of parallel sides, if any, does the quadrilateral have? _
So, quadrilateral ABCD is a ___ and a ___.
Classify the quadrilateral in as many ways as possible. Write
quadrilateral, trapezoid, parallelogram, rectangle, rhombus, or square.
2.
3.
Math
Talk
On
On Your
Your Own
Own
Math Processes and Practices 3
Make Arguments Can a
trapezoid have more than
one pair of parallel sides
that have the same length?
Explain your answer.
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Classify the quadrilateral in as many ways as possible. Write
quadrilateral, trapezoid, parallelogram, rectangle, rhombus, or square.
4.
5.
6.
7.
Chapter 11 • Lesson 3 651
Math Processes and Practices
COMMUNICATE • PERSEVERE • CONSTRUCT ARGUMENTS
Problem
Problem Solving
Solving •• Applications
Applications
8. A quadrilateral has exactly 2 congruent sides. Which quadrilateral types
could it be? Which quadrilaterals could it not be?
9.
10.
SMARTER
A quadrilateral has exactly 3 congruent sides. Davis
claims that the figure must be a rectangle. Why is his claim incorrect?
Use a diagram to explain your answer.
Math Processes
and Practices
3 Make Arguments The opposite corners of a quadrilateral
are right angles. The quadrilateral is not a rhombus. What kind of
quadrilateral is this figure? Explain how you know.
DEEPER
I am a figure with four sides. I can be placed in the following
categories: quadrilateral, trapezoid, parallelogram, rectangle, rhombus,
and square. Draw me. Explain why I fit into each category.
Personal Math Trainer
12.
SMARTER
For 12a–12c, write the name of one quadrilateral
from the tiles to complete a true statement. Use each quadrilateral
only once.
12a. A __ is sometimes a square.
12b. A __ is always a rectangle.
12c. A parallelogram is always a __.
652
square
trapezoid
rhombus
© Houghton Mifflin Harcourt Publishing Company
11.
Practice and Homework
Name
Lesson 11.3
Quadrilaterals
Learning Objective You will describe and
classify each type of quadrilateral and use a
Venn diagram to sort quadrilaterals to find
how they are related.
Classify the quadrilateral in as many ways as possible.
Write quadrilateral, trapezoid, parallelogram, rectangle, rhombus, or square.
2.
1.
quadrilateral
.
It has 4 sides, so it is a __
None of the sides are parallel, so there is
no other classification.
____
.
3.
______
4.
______
5.
______
6.
______
______
Problem
Problem Solving
Solving
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7. Kevin claims he can draw a trapezoid with three
right angles. Is this possible? Explain.
9.
8. “If a figure is a square, then it is a regular
quadrilateral.” Is this true or false? Explain.
______
______
______
______
______
______
WRITE
Math All rectangles are parallelograms. Are all parallelograms
rectangles? Explain.
Chapter 11 653
Lesson Check
1. Complete the following statement. Write
sometimes, always, or never.
A trapezoid ____ has
exactly one pair of parallel sides.
2. Complete the following statement. Write
sometimes, always, or never.
A rhombus ____ has four
congruent angles.
Spiral Review
4. The sides of a triangle measure 6 inches,
8 inches, and 10 inches. The triangle has
one 90° angle. What type of triangle is it?
5. A warehouse has 355 books to ship. Each
shipping carton holds 14 books. How many
cartons does the warehouse need to ship all
of the books?
6. How many vertices does a heptagon have?
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3. How many kilograms are equal to 5,000 grams?
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