2.4AnglePropertiesinPolygons.notebook
October 24, 2012
Section 2.4
Angle Properties in Polygons
Goal: Determine properties of angles in polygons,
and use these properties to solve problems.
May 9­10:17 AM
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How is the number of sides in a polygon
related to the sum of its interior angles
and the sum of its exterior angles?
Fill in the blanks of the following chart and
determine a pattern to find the sum of the
interior angles of any polygon.
Jun 21­2:07 PM
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Polygon
Number of
Sides
Triangle
3
Quadrilateral
4
Pentagon
5
Hexagon
6
Heptagon
7
Octagon
8
Number of Sum of Angle
Triangles
Measures
1
180°
Write a conjecture for the sum of the
interior angles of a polygon.
Jun 21­2:04 PM
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The formula to calculate the sum
of the interior angles of a
polygon is:
0
S = (n - 2) x 180
where n = the number of sides.
Jun 21­2:09 PM
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Regular polygon: a polygon all of whose sides
are the same length and all of whose interior
angles are the same measure.
Jun 22­9:09 AM
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Determine the sum of the interior
angles of a regular decagon (10sided shape).
Jun 21­2:12 PM
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What is the measure of each of
a regular decagon‛s interior
angles?
Jun 21­2:13 PM
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The angle sum of a polygon is 2160°.
Determine the number of sides of the
polygon.
Jun 22­9:04 AM
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Each interior angle of a regular polygon is
162°. Show that the polygon has 20 sides.
Jun 22­9:05 AM
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Determine the measure of each interior
angle of a regular 15 sided polygon
(pentadecagon).
Jun 22­9:13 AM
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Investigating the EXTERIOR Angle Sum
of Polygons
Find the exterior angles in each diagram
below. (not drawn to scale)
Jun 21­2:17 PM
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Jun 22­9:32 AM
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Use inductive reasoning to make a
conjecture about the exterior angle
sum of a polygon.
Jun 21­2:19 PM
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Use deductive reasoning to prove your
conjecture.
Jun 21­2:22 PM
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Example Proof (Can be extended for any polygon)
Given: ΔABC
Prove:
Statement
Justification
Supplementary Angles
formed by Straight Line
Addition Property
Triangle Sum Theorem
Subtraction Property
Jun 22­9:59 AM
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Convex Polygon: a polygon in which each
interior angle measures less than 1800.
Concave Polygon (non-convex): a polygon with
one or more interior angles greater than 1800.
Jun 21­2:23 PM
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A floor tiler designs custom floors using
tiles in the shape of regular polygons. Can a
tiling pattern be created using regular
hexagons and equilateral triangles that have
the same side length? Explain.
Sum of angles in a hexagon:
Each angle in a regular hexagon:
S = 180(n - 2)
= 180(6 - 2)
= 180(4)
= 7200
7200÷6 = 1200
Each angle in a equilateral triangle is 600.
Two hexagons and two triangles put together:
The angle at the common vertices will be 3600.
Jun 22­10:26 AM
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To summarize our results from our previous
investigations:
Interior angle
sum of a convex
polygon:
0
(n-2) x 180
Exterior angle sum
of a convex polygon:
0
360
Interior angle of
a regular convex
polygon:
(n-2) x 1800
n
Jun 22­9:14 AM
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2.4 Assignment: Nelson Foundations of Mathematics 11, Sec 2.4, pg, 99‐103
Questions: 1‐5, 7‐9, 11, 13, 14, 16
Jun 22­8:39 AM
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