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Warm-Up #28 Monday 5/2
1. Solve for x
2. Find AB
Warm-Up #29 Tuesday, 5/3
1. Prove why they are similar
and then solve for x.
2. Solve for x and y
Warm-up #30 Friday, 5/6
Warm-Up#31
1. To estimate the height of a tree, Dave stands in the shadow of the tree so that
his shadow and the tree’s shadow end at the end point. Dave is 5 feet 2 inches tall
and his shadow is 12 feet long. If he is standing 40 feet away from the tree, what is
the height of the tree?
2. In the triangle below, line segment MN is parallel to line segment BC. Solve for x.
Warm-Up #32
1. Solve for x and find all of the missing angles.
2. In triangle JKL, JK=15, JM = 5, LK = 13, and PK = 9. Determine
whether line segment JL is parallel to line segment MP. Justify your
answer.
Homework
Interior and Exterior Angles of Polygons
Naming Polygons
closed figure in a plane formed by segments, called sides.
A polygon is a _____________
A polygon is named by the number of its sides
_____ or angles
______.
tri means three.
A triangle is a polygon with three sides. The prefix ___
Naming Polygons
Prefixes are also used to name other polygons.
Prefix
Number of
Sides
Name of
Polygon
tri-
3
triangle
quadri-
4
quadrilateral
penta-
5
pentagon
hexa-
6
hexagon
hepta-
7
heptagon
octa-
8
octagon
nona-
9
nonagon
deca-
10
decagon
Naming Polygons
A vertex is the point
of intersection of
two sides.
Consecutive vertices are
the two endpoints of any
side.
Q
P
R
U
A segment whose
endpoints are
nonconsecutive
vertices is a
diagonal.
T
S
Sides that share a vertex
are called consecutive
sides.
An equilateral polygon has all sides
_____ congruent.
angles congruent.
An equiangular polygon has all ______
equiangular
equilateral and ___________.
A regular polygon is both ___________
equilateral
but not
equiangular
equiangular
but not
equilateral
regular,
both equilateral
and equiangular
Investigation: As the number of sides of a series of regular polygons increases, what do you
notice about the shape of the polygons?
The sum of the interior angle of a triangle
https://www.youtube.com/watch?v=DiwH-t9oaCg
Diagonals and Angle Measure
Make a table like the one below.
1) Draw a convex quadrilateral.
2) Choose one vertex and draw all
possible diagonals from that vertex.
3) How many triangles are formed?
Convex
Polygon
Number
of Sides
quadrilateral
4
Number of Diagonals
from One Vertex
1
Number of
Triangles
2
Sum of
Interior Angles
2(180) = 360
Diagonals and Angle Measure
1) Draw a convex pentagon.
2) Choose one vertex and draw all
possible diagonals from that vertex.
3) How many triangles are formed?
Convex
Polygon
Number
of Sides
Number of Diagonals
from One Vertex
Number of
Triangles
Sum of
Interior Angles
quadrilateral
4
1
2
2(180) = 360
pentagon
5
2
3
3(180) = 540
Diagonals and Angle Measure
1) Draw a convex hexagon.
2) Choose one vertex and draw all
possible diagonals from that vertex.
3) How many triangles are formed?
Convex
Polygon
Number
of Sides
Number of Diagonals
from One Vertex
Number of
Triangles
Sum of
Interior Angles
quadrilateral
4
1
2
2(180) = 360
pentagon
5
2
3
3(180) = 540
hexagon
6
3
4
4(180) = 720
Diagonals and Angle Measure
1) Draw a convex heptagon.
2) Choose one vertex and draw all
possible diagonals from that vertex.
3) How many triangles are formed?
Convex
Polygon
Number
of Sides
Number of Diagonals
from One Vertex
Number of
Triangles
Sum of
Interior Angles
quadrilateral
4
1
2
2(180) = 360
pentagon
5
2
3
3(180) = 540
hexagon
6
3
4
4(180) = 720
heptagon
7
4
5
5(180) = 900
Diagonals and Angle Measure
1) Any convex polygon.
2) All possible diagonals from one vertex.
3) How many triangles?
Convex
Polygon
Number
of Sides
quadrilateral
4
1
2
2(180) = 360
pentagon
5
2
3
3(180) = 540
hexagon
6
3
4
4(180) = 720
heptagon
7
4
5
5(180) = 900
n-gon
n
n-3
n-2
(n – 2)180
Theorem
Number of Diagonals
from One Vertex
Number of
Triangles
Sum of
Interior Angles
If a convex polygon has n sides, then the sum of the
measure of its interior angles is (n – 2)180.
If a convex polygon has n sides, then the
Theorem
sum of the measure of its interior angles is
of interior
(n – 2)180.
angles
Ex. 1: Finding measures of Interior Angles of Polygons
• Find the value of x in the diagram
shown:
142
88
136
105
136
x
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SOLUTION:
• The sum of the
measures of the interior
angles of any hexagon is
(6 – 2) ● 180 = 4 ● 180
= 720.
• Add the measure of
each of the interior
angles of the hexagon.
142
88
136
105
136
x
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SOLUTION:
136 + 136 + 88 + 142 +
105 +x = 720.
The sum is 720
607 + x = 720
Simplify.
X = 113
Subtract 607 from each
side.
•The measure of the sixth interior angle of the hexagon is
113.
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EXTERIOR ANGLE THEOREMS
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EXTERIOR ANGLE THEOREMS
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Ex. 2: Finding the Number of Sides of a Polygon
• The measure of each interior angle is 140. How many sides does the
polygon have?
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Solution:
( n  2)(180)
n
= 140
(n – 2) ●180= 140n
Corollary to Thm. 11.1
Multiply each side by n.
180n – 360 = 140n
40n = 360
n=9
Distributive Property
Addition/subtraction props.
Divide each side by 40.
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Ex. 3: Finding the Measure of an Exterior Angle
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Ex. 3: Finding the Measure of an Exterior Angle
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Ex. 3: Finding the Measure of an Exterior Angle
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Using Angle Measures in Real Life
Ex. 4: Finding Angle measures of a polygon
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Using Angle Measures in Real Life
Ex. 5: Using Angle Measures of a Regular Polygon
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Using Angle Measures in Real Life
Ex. 5: Using Angle Measures of a Regular Polygon
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Using Angle Measures in Real Life
Ex. 5: Using Angle Measures of a Regular Polygon
Sports Equipment: If you were designing the
home plate marker for some new type of ball
game, would it be possible to make a home
plate marker that is a regular polygon with
each interior angle having a measure of:
a. 135°?
b. 145°?
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Using Angle Measures in Real Life
Ex. : Finding Angle measures of a polygon
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