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Classifying Quadrilaterals
BEFORE
Now
WHY?
You classified triangles by their
angles and sides.
You’ll classify quadrilaterals
by their angles and sides.
So you can classify figures in
woodwork, as in Exs. 19–21.
Quadrilaterals A quadrilateral is a plane figure
Word Watch
quadrilateral, p. 445
parallelogram, p. 445
rectangle, p. 445
rhombus, p. 445
square, p. 445
formed by 4 segments called sides. Each side intersects
exactly 2 other sides, one at each endpoint, and no two
sides are part of the same line. The chart below shows
some types of quadrilaterals.
Special Quadrilateral
Diagram
A parallelogram is a quadrilateral with
2 pairs of parallel sides.
A rectangle is a parallelogram with
4 right angles.
A rhombus is a parallelogram with
4 sides of equal length.
A square is a parallelogram with
4 right angles and 4 sides of
equal length.
EXAMPLE
with
Notetaking
Try making a Venn
diagram in your notebook
to help you organize the
different types of
quadrilaterals. For help
with Venn diagrams,
see p. 703.
1
Classifying Quadrilaterals
Tell whether the statement is true or false. Explain your reasoning.
a. All squares are rectangles.
b. Some rhombuses do not have 2 pairs of parallel sides.
Solution
a. True: All squares are parallelograms with 4 right angles, so all
squares are rectangles.
b. False: All rhombuses are parallelograms, so all rhombuses have
2 pairs of parallel sides.
Lesson 9.5
Classifying Quadrilaterals
445
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Classify Parallelograms You need to look at all the marks
and labels on a parallelogram to decide how to classify it. Some
parallelograms can be classified in more than one way.
EXAMPLE
2
Classifying Parallelograms
Classify the parallelogram in as many ways as possible.
a.
b.
5m
c.
3m
3m
3 yd
3 yd
4 in.
3 yd
3 yd
5m
Solution
a. The parallelogram is a rectangle because it has 4 right angles.
b. The parallelogram is a rectangle, a rhombus, and a square
because it has 4 right angles and 4 sides of equal length.
c. The parallelogram is a rhombus because it has 4 sides of
equal length.
EXAMPLE
3
Drawing a Quadrilateral
Draw a quadrilateral that is a rectangle but not a square.
1 Draw one side.
Your turn now
1.
2 Draw a right
angle. Then draw
a side with a
different length.
3 Draw two more
right angles. Then
draw the other
two sides and angle.
Classify the quadrilateral in as many ways as possible.
2.
5 cm
3.
3 ft
3 cm
3 cm
5 cm
5 ft
4. Draw a parallelogram that is neither a rectangle nor a rhombus.
446
Chapter 9
Geometric Figures
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INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 716
Getting Ready to Practice
Vocabulary Copy and complete the statement.
1. A rhombus is a _?_ with 4 sides of equal length.
2. A _?_ is a parallelogram with 4 sides of equal length and 4 right angles.
Tell whether the statement is true or false. Explain your reasoning.
3. A square is always a rhombus.
4. All squares have 4 right angles.
Quilts Classify the quadrilateral in as many ways as possible.
5.
6.
7.
Practice and Problem Solving
Copy and complete the statement using All or Some.
8. _?_ rectangles are squares.
9. _?_ rhombuses are parallelograms.
10. _?_ squares are rhombuses.
11. _?_ parallelograms are squares.
Classify the parallelogram in as many ways as possible.
with
Example
1
2
3
Homework
Exercises
8–11
12–14
15
12.
13.
14.
7m
7m
7m
7m
15. Draw a rhombus that is not a square.
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial Plus
Critical Thinking Identify all quadrilaterals that always fit
the description.
16. 4 equal sides
17. 4 right angles
Lesson 9.5
18. 2 pairs of parallel sides
Classifying Quadrilaterals
447
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Woodworking Use the woodwork shown.
1
2
19. Classify the numbered quadrilaterals.
20. What type of quadrilateral is the
3
entire woodwork?
21. How many rhombuses that are not
squares are shown on the woodwork?
Algebra The sum of the angle measures of a quadrilateral is 360.
Use this information to find the value of x.
22.
112
x
96
23.
24.
62
103
x
86
77
106
x
103
25. Writing Explain why a rhombus that is also a square is always
a rectangle.
26. Challenge Is it possible to draw a quadrilateral that has 2 right angles
but is not a rectangle? Is this possible with 3 right angles? Explain.
Mixed Review
2
27. Order the numbers 42%, 0.45, and from least to greatest. (Lesson 8.6)
5
Tell whether the angle measures are those of a triangle. If so, classify
the triangle as acute, right, or obtuse. (Lesson 9.4)
28. 28, 38, 124 29. 20, 80, 80
30. 23, 55, 102 31. 45, 45, 90
Basic Skills Find the total amount spent.
32. 7 light bulbs for $1.50 each
33. 4 bags of pretzels for $2.75 each
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
34. Multiple Choice Which figure is not a parallelogram?
A.
B.
C.
D.
35. Short Response Explain why a square is a rectangle, a rhombus, a
parallelogram, and a quadrilateral.
448
Chapter 9
Geometric Figures