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November 17, 2017
number of sides
Name of polygon
3
4
5
6
7
8
10
n
triangle
quadrilateral
pentagon
hexagon
heptagon
octagon
decagon
n-gon
Warmup:
Complete the table by naming each polygon.
November 17, 2017
Do not need to know just fun to know...
November 17, 2017
Geometry Section 5.1
Polygons &
their angle measures
Learning Target:I can calculate angle measure for angles of polygons. [G.MG.1]
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polygon NOT a polygon
Polygon - a ________ plane figure with 3 or more __________ sides
and each vertex connects only ___________.
November 17, 2017
A polygon is convex if no line that contains a side of the polygon passes through the interior of the polygon.
A polygon that is not convex is called concave.
How can you remember concave?
November 17, 2017
polygon not a polygon convex concave
Tell whether the figure is a polygon and whether it is convex or concave.
a. b.
c. d.
(name the logo)
November 17, 2017
A polygon is
all interior angles ≅
all sides ≅ AND all int angles ≅
all sides ≅equilateral -
equiangular -
regular -
Equilateral EquiangularRegular
November 17, 2017
equilateral regular
Classify the polygon by the number of sides. Tell whether the polygon is equilateral, equiangular or regular. Explain your reasoning.
a. b.
c.
equiangular
d.
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Activity: Exploring the Sum of the Interior and Exterior Angles of convex polygons
November 17, 2017
POLYGON INTERIOR ANGLES THEOREMThe sum of the measures of the interior angles of a convex polygon with n sides is
POLYGON EXTERIOR ANGLES THEOREMThe sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is ________.
m∠1 + m∠2 + m∠3 + m∠4 + m∠5 = 360
http://www.mathsisfun.com/geometry/exterior-angles-polygons.html
SUM Interior ∠s = (n – ___ ) _______
SUM Exterior ∠s = ______
November 17, 2017
2) The sum of the interior angles of a polygon is 1980˚, classify the polygon by the number of sides.
1) Find the sum of the interior angles of
a) decagon b) 15-gon
November 17, 2017
xo
(x + 20)˚
112˚96o
4) Find the value of x.
3) Find the value of x.Hint: find the sum of the interior angles first
Hint: find the sum of the exterior angles first
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5) Find the measure of one interior ∠ AND one exterior ∠ on a stop sign.
6) Each interior angle of the regular n-gon has a measure is 162˚. Find the value of n.
November 17, 2017
Homework:5.1 Angles in Polygons
Sum Interior = (n – 2) • 180
Sum Exterior = 360˚
In a Regular Polygon
Each Interior =n
(n – 2) •180
Each Exterior = n 360
Assignment: 5.1 worksheet
November 17, 2017
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