Download Regular Polygon - Shope-Math

Geometry
3 Dec 2012
1) Empty folders and place papers in correct
section in your binder.
2) Place book and binder on your desk.
3) DO Flow Chart Proof Handout, # 3
Finished? Do 4.6 CPCTC handout, #12.
Finished? Choose one proof from handout
and rewrite in a 2nd “style”.
objective
Students will apply polygon interior and exterior
sum conjectures to find angle measures.
Students will take notes, work collaboratively
and present to the class.
Homework due Dec 4
5.1, pg 259: 3 – 8
5.2, pg. 264: 8 – 13, 16, 17
Inductive Reasoning
the process of
OBSERVING
FINDING PATTERNS
MAKING GENERALIZATIONS…
GEOMETRY the generalization is called
A CONJECTURE!!!
Conjecture is an IF…THEN… statement
Exterior angle
Vertex
Side
Diagonal
Polygons
Interior angle
• Equiangular: all angles have
equal measure
• Equilateral: all sides are the
same length
Polygons
• Regular Polygon: a
polygon where all the
angles are equal and all of
the sides are the same
length. They are both
equilateral and equiangular
Polygons
Examples of Regular Polygons
Polygons
Exterior Angles of a Polygon
Is there a pattern for the sum for exterior angles
of polygons?
DEMONSTRATION
What about a octagon?
What is the measure of ONE exterior angle for
a regular quadralateral? regular pentagon?
http://math.kendallhunt.com/x19427.html
No matter what type of
polygon we have, the sum
of the exterior angles is
ALWAYS equal to 360º.
Sum of exterior angles =
360º
Polygons
180
180o
180o
180
o
o
180o
4 sides
Quadrilateral
5 sides
2 x 180o = 360o
2
Pentagon
o
1 diagonal
o
3 x 180 = 540
3
2 diagonals
180o
180o
180o
180o
180o
180o
180o
180o
180o
6 sides
4
Hexagon
4 x 180o = 720o
3 diagonals
Polygons
7 sides
5
Heptagon/Septagon
5 x 180o = 900o
4 diagonals
Rule?
Can you find a rule for the interior angle sum for
an “N”-gon?
What if you have a regular polygon?
Regular Polygonall sides and angles have the same measure
Polygons
Term
Polygon
Sum
Conjecture
Definition
The sum of the measures of
the interior angles of an
n-gon is
180  n  2 
0
Exterior
angle sum
conjecture
For any polygon, the
sum of the measures of
a set of external angles
is 3600
Equiangular
Polygon
Conjecture
Each interior angle of an
equiangular n-gon
1800  n  2 
n
Example
Sum of interior
angles
1800  n  2 
1800  n  2 
n
Find the unknown angles below.
w
100o
2 x 180o = 360o
360 – 245 = 115o
140o
125o
100o
121o
117o
Polygons
x
75o
75o
70o
y
4 x 180o = 720o
720 – 603 =
117o
Diagrams not
drawn
accurately.
95o
115o
110o
3 x 180o = 540o
540 – 395 =
145o
125o
z
138o
138o
133o
105o
137o
5 x 180o = 900o
900 – 776 =
124o
Practice– Homework Problems
CW Focus:
In progress: 5.1: 3, 4
5.2: 8
Partial: 5.1: 5, 6
5.2: 9
Complete: 5.1: 7, 8
5.2: 10
Advanced: 5.1: 7
5.2: 10, 13
Debrief
What is difficult about finding angle measures in
an “angle chase”?
What strategies can you use?
What is easy?