Download 3-5 Polygons Presentation

Warm Up:
Given: a // b
Prove:
m6 = m9
m9 = m2
Statements
Diagram:
a
b
1
2
3 4
5 6
7 8
t
Reasons
9
Examples
Not Polygons
Convex Polygon – any polygon such that
no line segment can be drawn between
two vertices on the exterior of the
polygon.
Convex
Not Convex
Regular Polygon – a polygon that is both
equilateral and equiangular.
Diagonal – a segment joining two
nonconsecutive vertices of a convex
polygon.
Angle Measures in Polygons
You can find the sum of the interior angles
of a polygon by dividing a convex polygon
into triangles – do this by drawing all
diagonals from ONE vertex.
5 sided figure can
be broken into 3
triangles.
Therefore the sum
of the angles would
be 3 x 180 = 540
Angle Measures in Polygons
If you try this several times, you can use
INDUCTIVE REASONING to hypothesize
that…
6 sided figure can be
broken into 4 triangles.
4 sided figure can be
4 x 180 = 720
broken into 2 triangles.
2 x 180 = 360
The sum of the measures
of the angles of a convex
polygon with n sides is
(n – 2) x 180.
A hexagon has 6 sides. What would the sum of the
measures of the angles of a hexagon be?
What would the measure of
(6 – 2) x 180
each angle be if the
720°
hexagon was regular?
720  6 = 120
Exterior angle activity
The sum of the measures
of the exterior angles of
any convex polygon, one
angle at each vertex, is
60°
360°
60° 120° 120°
60°
120°
60°
120°
60°
120°
120° 60°
6(60) = 360
Number
of Sides
Name
Sum of Interior
Angles
Measure of
each angle (if the
Sum of
Exterior
Angles
polygon is regular)
3
Triangle
180°
60°
360°
4
Quadrilateral
360°
90°
360°
5
Pentagon
540°
108°
360°
6
Hexagon
720°
120°
360°
7
Heptagon
900°
128.57°
360°
8
Octagon
1080°
135°
360°
9
Nonagon
1260°
140°
360°
10
Decagon
1440°
N
n-gon
144°
(n - 2)x180° (n  2)  180
n
360°
360°
Ticket to leave
1.) Given a 12 sided polygon, find the sum
of the measure of the interior and
exterior angles.
2.) Draw a convex polygon and draw a
nonconvex polygon.
Unit 3 Test of Monday.
Please come prepared for class on Friday
with questions.
Due Friday:
Packet pg 14
p. 111-112 Chapter Review #1-19
(skip 16a) Draw Diagrams!