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LESSON
6.1
NAME _________________________________________________________ DATE ____________
Reteaching with Practice
For use with pages 303–308
GOAL
Identify and classify polygons. Find angle measures
of quadrilaterals.
VOCABULARY
A polygon is a plane figure that is formed by three or more segments
called sides. The endpoint of each side is a vertex.
Lesson 6.1
A segment that joins two nonconsecutive vertices of a polygon is called
a diagonal.
Polygons are classified by the number of sides they have. A triangle has
three sides. A quadrilateral has four sides. A pentagon has five sides. A
hexagon has six sides. A heptagon has seven sides. An octagon has
eight sides.
Theorem 6.1 Quadrilateral Interior Angles Theorem
The sum of the measures of the interior angles of a quadrilateral is 360.
EXAMPLE 1
Identify Polygons
Tell whether the figure is a polygon. Explain your reasoning.
a.
b.
c.
SOLUTION
a. No, the figure is not a polygon because each side intersects two other sides at one
vertex, and no other sides at the other vertex.
b. No, the figure is not a polygon because it has a side that is not a segment.
c. Yes, the figure is a polygon formed by five straight sides.
Exercises for Example 1
Tell whether the figure is a polygon. Explain your reasoning.
1.
2.
4.
5.
Copyright © McDougal Littell Inc.
All rights reserved.
3.
Geometry
Chapter 6 Resource Book
13
cgrb-0601.qxd
11/12/01
LESSON
6.1
CONTINUED
EXAMPLE 2
11:03 AM
Page 14
NAME _________________________________________________________ DATE ____________
Reteaching with Practice
For use with pages 303–308
Classify Polygons
Decide whether the figure is a polygon. If so, tell what type. If not, explain why.
a.
b.
c.
Lesson 6.1
SOLUTION
a. The figure is a polygon with seven sides, so it is a heptagon.
b. The figure is not a polygon because two of the sides intersect only one other side.
c. The figure is a polygon with six sides, so it is a hexagon.
Exercises for Example 2
Decide whether the figure is a polygon. If so, tell what type. If
not, explain why.
6.
EXAMPLE 3
7.
8.
Use the Quadrilateral Interior Angles Theorem
Find the value of x.
B
118
A
SOLUTION
84 C
50
2x Use the fact that the sum of the measures of the interior
angles of a quadrilateral is 360.
ma A ma B ma C ma D 360
50 118 84 2x 360
252 2x 360
2x 108
x 54
D
Quadrilateral Interior Angles Theorem
Substitute angle measures.
Simplify.
Subtract 252 from each side.
Divide each side by 2.
Exercises for Example 3
Find the value of x.
9.
10.
B
E
74
(x 5) C
A 106
110
D
14
Geometry
Chapter 6 Resource Book
G
81
F
11.
K
J
(11x)
75
H
M
(9x 3)
108 120 L
Copyright © McDougal Littell Inc.
All rights reserved.