Download Polygons

Geometry
Name: ________________________ Date: _____________ Period: _____
Front_Day1: Polygons
Back_Day 2: Regular Polygons
Day 3: Formulas for Polygons
Polygon: _________________________________________________________________________________.
Convex Polygons (same as a Convex Quadrilateral): _______________________________________________.
Concave Polygon (same as a Concave Quadrilaterals): _____________________________________________.
Have you ever asked yourself the following questions?
Why is a 3-sided polygon called a triangle instead of a tri-gon? Why is a 4-sided polygon called a quadrilateral
instead of a tetragon, when all the others are ___-gons? Why is there not a single consistent term?
Well there really is no answer on why, but it just happened to happen that way. GREAT ANSWER, HUH?
"________________" uses the Latin "angle" (angulus) rather than the Greek "gon" which means the same thing,
so it's just the Latin equivalent of the Greek "trigon."
"________________" is even more distinctive, since it not only comes from Latin but means "four sides" rather
than "four angles"
The thought is that triangle and quadrilateral came to be in the English Language at a different time then words
that use –gon, like polygon, hexagon, and others. SO, -gon means __________, and the following prefixes are
add to show how many sides a polygon has.
____________-gon: has 3 sides ( _____________ )
____________-gon: has 10 sides
____________-gon: has 4 sides ( _____________ )
____________-gon: has 11 sides
____________-gon: has 5 sides
____________-gon: has 12 sides
____________-gon: has 6 sides
____________-gon: has 13 sides or ______________
____________-gon: has 7 sides
____________-gon: has 14 sides
____________-gon: has 8 sides
____________-gon: has 15 sides or
____________-gon: has 9 sides
________________ or ________________
I’m going to assign each of you a polygon that I want you to draw using a straight edge. Once you have drawn
your polygon measure all of the interior angles and find the sum of those angles. Also measure the exterior
angles and find that sum. We will then come make together and fill in the table below and find the pattern that
exists between the number sides and the sum of the interior angles of a polygon and between the number of
sides and the sum of the exterior angles. We should be able to fill in the first two columns quickly.
Sides
3
4
5
Int.
Ang.
Sum
Ext.
Ang.
Sum
Polygon Sum Conjecture:
6
7
8
The sum of the measures of the n interior angles of
an n-gon is
9
10
11
12
15
For any polygon, the sum of the measures of a set of
exterior angles is
a
70°
140°
60°
110°
116°
68°
14
Exterior Angle Sum Conjecture:
Examples of each conjecture: Find the missing angles measurement.
b
13
68°
84°
16
HW_Polygons
Name: _______________________ Date: _____________ Pd: _____
Find the value of the unknown variables:
76°
h
66°
1)
2)
d
3)
c
72°
30°
a
44°
108°
117°
130°
g
78°
43°
4)
5)
60°
m
140°
68°
69°
z
84°
68°
7) What’s wrong with this picture?
8) What’s wrong with this picture?
82°
154°
102°
135°
49°
76°
8) How many sides does a polygon have if the sum of its interior angle measures is 7380°?
9) The interior angle sum of a convex polygon is 5 times its exterior angle sum. What kind of polygon is it?
10) If the interior angle sum of a convex polygon is 2520°, then how many sides does it have?
11) The interior angles of a pentagon are x, x, 2x, 2x, and 2x. What is the measure of the larger angles?
12) The exterior angles of a quadrilateral are x, 2x, 3x and 4x. What is the measure of the smallest angle?
13) A baseball diamond’s home plate has three right angles. The remaining two angles are congruent. What are
their measures?
14) Is there a maximum number of obtuse exterior angles that any polygon can have? If so, what if the
maximum? If not, why not? Is there a minimum number of acute interior angles that any polygon must have? If
so, what is the minimum? If not, why not?