The Polygon Angle-Sum Theorems Worksheet With Answers
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8The Polygon Angle-Sum
3-5
3-5
3-5
3-5
Theorems
1. Plan
Objectives
What You’ll Learn
GO
for Help
Check Skills You’ll Need
Lessons 1-6 and 3-4
1
To classify polygons
•
To classify polygons
Find the measure of each angle of quadrilateral ABCD.
2
To find the sums of the
•
See below.
To find the sums of the
measures of the interior and
See below.
1.
2.
3.
A
B
A
B
B
measures of the interior
exterior angles of polygons
55
65
and exterior angles of
A
45
30
polygons
Examples
70
32
1
Naming Polygons
. . . And Why
C
55
C
2
Real-World Connection
D
C
To find the measure of an
87
61
25
3
Finding a Polygon Angle Sum
m l D
m l B
60;
angle of a triangle used in
D
D
m l DAB
m l DCB
4
Using the Polygon Angle-Sum
packaging, as in Example 5
120
Theorem
New Vocabulary •
polygon
•
convex polygon
•
concave polygon
5
Real-World Connection
•
•
equilateral polygon
equiangular polygon
•
regular polygon
3. m l A
70; m l ABC
85;
m l C
125; m l ADC
1. m l DAB
77; m l B
80
65;
Math Background
m l BCD
131; m l D
87
1 1
Classifying Polygons
Because each interior angle
of a regular n-gon measures
180 (n 2 2)
, one can readily find
n
A
polygon
is a closed plane figure with at least three sides that are segments. The
the set of all regular n-gons that
sides intersect only at their endpoints, and no adjacent sides are collinear.
tesselate a plane. Combinations
of regular polygons that tesselate
B
B
B
a plane can likewise be found with
A
A
A
a bit more work and application
C
C
C
of some straightforward number
theory.
E
D
E
D
D
E
More Math Background:
p. 124D
A polygon
Not a polygon;
Not a polygon;
not a closed figure
two sides intersect
Real-World
Connection
between endpoints.
Lesson Planning and
Polygons create striking
To name a polygon, start at any vertex and list the vertices consecutively in a
designs on a soccer ball.
Resources
clockwise or counterclockwise direction.
See p. 124E for a list of the
resources that support this lesson.
1
1
EXAMPLE
Naming Polygons
EXAMPLE
Name the polygon. Then identify its vertices, sides, and angles.
D
H
PowerPoint
Bell Ringer Practice
Two names for this polygon are DHKMGB and MKHDBG.
B
K
vertices: D, H, K, M, G, B
Check Skills You’ll Need
DH
HK
KM
MG
GB
BD
sides:
,
,
,
,
,
For intervention, direct students to:
G
M
angles: &D, &H, &K, &M, &G, &B
Using the Angle Addition
B
Quick Check
C
Postulate
1
1
Three polygons are pictured at
A
Lesson 1-6: Example 3
the right. Name each polygon,
Extra Skills, Word Problems, Proof
D
its sides, and its angles.
See margin, p.159.
E
Practice, Ch. 1
157
Lesson 3-5
The Polygon Angle-Sum Theorems
Finding Angle Measures in
Triangles
Lesson 3-4: Example 1
Extra Skills, Word Problems, Proof
Special Needs
Below Level
L1
L2
Practice, Ch. 3
Have students draw a polygon with an exterior angle
Have students draw a polygon on paper and cut out
at each vertex. Students cut out their exterior angles
the exterior angles. By placing the angles so that they
and tape the vertices together. Students should
are adjacent, students can verify Theorem 3-15.
recognize the sum of the exterior angles is 360°.
learning style: tactile
learning style: tactile
157
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