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Bellwork
Brain teaser (think about):
What are the next 2 numbers in the sequence?
93 ___.
186
3, 6, 9, 18, 21, 42, 45, 90, ___,
Pattern: multiply by 2, then add 3. Repeat ad infinitum.
Bellwork
Brain teaser: which sentence below is different than the rest?
a)
b)
c)
d)
Do geese see God?
The brown fox jumped over the poodle.
Was it a car or a cat I saw?
Rats live on no evil star.
The other 3 sentences are palindromic (they are palindromes:
they read the same forward and backward).
Polygons!
closed
Polygon: A ______________
figure in a plane made
segments
of 3 or more _____________________.
Convex polygons:
Concave polygons:
dent
Polygons
Regular polygon: all sides and angles congruent.
Apothem:
(Always at a right
angle through the
midpoint of a side)
Regular pentagon
Polygons
pentagon inside
the circle
Inscribed pentagon
Pentagon circling
the circle
Circumscribed pentagon
Names of Polygons
3 sides: triangle
4 sides: quadrilateral
5 sides: pentagon
6 sides: hexagon
7 sides: heptagon
8 sides: octagon
9 sides: nonagon
10 sides: decagon
On a Piece of Paper, draw:



Convex, irregular pentagon
An inscribed regular hexagon
Concave regular quadrilateral
 Impossible!


Any concave polygon
A circumscribed regular quadrilateral
Activity
5.1 Activity
Objectives

Content Objective:
 Compute
the sum of the interior angles of a regular
polygon

Language Objective:
 You
will be able to listen to the description and draw a
diagram of a polygon
Geometry Bellwork:

Take out an index card!
Sum of interior angles of a polygon:
S = 180(n – 2)
Sum of
interior
angles
Number of
sides
Sn = 180(n – 2)
Nonagon!
Sn = 180(9 – 2)
Sn = 180(7)
Sn = 1260
That was easy…
To find 1 interior angle of a regular
polygon


Find the measure of 1 interior angle of a regular
octagon.
Step 1
Find the sum of all 8 angles
S = 180(n – 2)
S = 180 (8 – 2)
S = 180(6)
Step
S = 1080
2:
Divide 1080 by 8 (the
number of angles)
= 135°
To find an exterior angle:

Find an exterior angle of a regular polygon
Steps:
1) Find the measure of 1 interior
angle
2) We just found that 1 interior
angle of a regular octagon is
135°
3) Since the interior and exterior
angles form a linear pair,
subtract 180 – 135.
4) The exterior angle is 45°.
135°
Sn = 180(6 – 2)
Sn = 180(4)
Sn = 720
Exterior
angle
Example…………
When referring to congruent triangles (or polygons), we must
name corresponding vertices in the same order.
R
Y
A
N
U
S
R
U
A
N
Y
RAY
SUN  ______
YAR
Also NUS  ______
ARY
Also USN  ______
S
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