Download 6.1 Practice with Examples

LESSON
6.1
NAME _________________________________________________________ DATE ____________
Practice with Examples
For use with pages 322–328
GOAL
Identify, name, and describe polygons and use the sum of the measures of
the interior angles of a quadrilateral
VOCABULARY
Chapter 6
A polygon is a plane figure that is formed by three or more segments
called sides, such that no two sides with a common endpoint are
collinear, and each side intersects exactly two other sides, one at each
endpoint. Each endpoint of a side is a vertex of the polygon.
A polygon is convex if no line that contains a side of the polygon
contains a point in the interior of the polygon.
A polygon that is not convex is called nonconvex or concave.
A diagonal of a polygon is a segment that joins two nonconsecutive
vertices.
Theorem 6.1 Interior Angles of a Quadrilateral
The sum of the measures of the interior angles of a quadrilateral is 360.
EXAMPLE 1
Identifying Polygons
State whether the figure is a polygon. If it is not, explain why.
A
C
D
B
SOLUTION
Figures A and C are polygons.
• Figure B is not a polygon because it only has two sides, and one of
its sides is not a segment.
• Figure D is not a polygon because two of the sides intersect only
one other side.
100
Geometry
Practice Workbook with Examples
Copyright © McDougal Littell Inc.
All rights reserved.
LESSON
6.1
CONTINUED
NAME _________________________________________________________ DATE ____________
Practice with Examples
For use with pages 322–328
Exercises for Example 1
State whether each figure is a polygon. If it is not, explain why.
1.
2.
A
3.
4.
B
D
C
Chapter 6
EXAMPLE 2
Identifying Convex and Concave Polygons
State whether each polygon
is convex or concave.
a.
b.
SOLUTION
a. The polygon has 5 sides. When
extended, none of the sides intersect
the interior, so the polygon is convex.
b. The polygon has 10 sides. When
extended, some of the sides intersect
the interior, so the polygon is concave.
Exercises for Example 2
State whether the polygon is convex or concave.
5.
Copyright © McDougal Littell Inc.
All rights reserved.
6.
7.
Geometry
Practice Workbook with Examples
101
LESSON
6.1
CONTINUED
EXAMPLE 3
NAME _________________________________________________________ DATE ____________
Practice with Examples
For use with pages 322–328
Interior Angles of a Quadrilateral
Find mA and mB.
C
SOLUTION
50
Find the value of x. Use the Interior Angles of a Quadrilateral
Theorem to write an equation involving x. Then solve the equation.
Chapter 6
5x 7x 50 70 360
x 20
B
7x Theorem 6.1
Solve for x.
So, mA 5x 520 100 and mB 7x 720 140.
A
5x
70
D
Exercises for Example 3
Use the information in the diagram to solve for x.
8.
x
9.
2x
3x
87
93
3x
2x
102
Geometry
Practice Workbook with Examples
Copyright © McDougal Littell Inc.
All rights reserved.