Download Interior and Exterior Angles of Polygons

Basics of Polygons
Introduction:
1) Define Polygon
2) Name 3 reasons why a geometric figure would not be a polygon
a.
b.
c.
3) Define side of a polygon.
4) Define vertex of a polygon.
5) Define diagonal of a polygon.
6) Define regular polygon
7) List the generic names of Polygons in order, by filling in the table below.
3 sides =
8 sides =
4 sides =
9 sides =
5 sides =
10 sides =
6 sides =
12 sides =
7 sides =
n sides =
DUE FRIDAY, MAY 1ST
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Basics of Polygons
8)
a. Discuss the difference between convex and concave polygons
b. Draw and label a picture of each in the space provided below
9) Match the following geometric term with its definition below
a. Parallelogram
i. A figure with 4 equal sides and 4 right angles
b. Rhombus
ii. A figure with 4 right angles and opposite sides
being the same length
d. Trapezoid
iii. A figure with 4 equal sides and opposite angles
being the same degree measurement
e. Rectangle
iv. A figure with 4 sides and only one set of those
sides are parallel
c. Square
v. A figure with 4 sides and two sets of those sides are
parallel, but angles may not be right
DUE FRIDAY, MAY 1ST
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Basics of Polygons
Investigation:
Part 1
In this investigation you are going to discover an easier way to find the sum of the
interior angles of a polygon, by dividing a polygon into triangles.
5
E
9) Consider the quadrilateral to the right.
Diagonal EG is drawn. A diagonal
is a segment connecting a vertex with a
nonadjacent vertex.
F
6
1
The quadrilateral is now divided into two
triangles, Triangle DEG and Triangle FEG.
Angles 1, 2, and 3 represent the interior angles
of Triangle DEG and Angles 4, 5, and 6
represent the interior angles of Triangle FEG.
D 2
m  1 + m  2 + m  3 = _________
3
4
G
m  4 + m  5 + m  6 = _________
m  1 + m  2 + m  3 + m  4 + m  5 + m  6 = _________
10) What is the relationship between the sum of the angles in the quadrilateral and the
sum of the angles in the two triangles?
By splitting any polygon into triangles you can find the sum of the interior
angles of the polygon.
11) Using the splitting triangle method find the sum of the interior angles of this
hexagon.
DUE FRIDAY, MAY 1ST
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Basics of Polygons
12) Draw a sketch of each polygon and use this same procedure to determine the sum
of the angles for each polygon in the table.
Polygon
Number of
Sketch
sides
Number of
Number of Interior angle
diagonals
triangles
sum
from 1 vertex
Triangle
3
0
1
180o
Quadrilateral
4
1
2
360o
Pentagon
Hexagon
Heptagon
Octagon
Decagon
Dodecagon
n-gon
DUE FRIDAY, MAY 1ST
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Basics of Polygons
13) In the last row of the table you should have developed a formula for finding the
sum of the interior angles of a polygon. Use this formula to find the sum of the
interior angles of a 20-gon.
14) Write a sentence explaining how to find the sum of the interior angles of a polygon.
Part 2
Regular Polygon
Nonregular Polygon
15) Compare the two polygons shown above.
How would you define a regular polygon and a nonregular polygon?
16) What is the sum of the interior angles of a hexagon?
17) What is the measure of one angle of a regular hexagon?
18) If you know the sum of the angles of a regular polygon, how can you find the
measure of one of the congruent angles?
DUE FRIDAY, MAY 1ST
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Basics of Polygons
19) Use the information from Part 1 to complete the table below:
Regular Polygon
Interior angle
sum
Triangle
180o
Quadrilateral
360o
Measure of
one angle
Pentagon
Hexagon
Heptagon
Octagon
Decagon
Dodecagon
n-gon
Problems:
20)
What is another name for a regular triangle?
21)
What is another name for a regular quadrilateral?
22)
What is the interior angle sum of a 60-gon?
23)
What is the measure of one interior angle of a regular 60-gon?
24)
Three angles of a quadrilateral measure 98 o, 75 o, 108 o.
Find the measure of the fourth angle.
DUE FRIDAY, MAY 1ST
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Basics of Polygons
25)
Each interior angle of a regular polygon measures 168 o.
How many sides does the polygon have?
26)
If the sum of the interior angles of a polygon is 1080 o .
How many sides does the polygon have?
27)
If the sum of the interior angles of a polygon is 1200 o .
How many sides does the polygon have? Is this polygon possible?
Webquest
HUNT FOR POLYGONS: an Internet Treasure Hunt on Polygons
(see attached page to begin)
DUE FRIDAY, MAY 1ST
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