Polygons
Triangles and Quadrilaterals
What is a polygon?
Closed figure
At least 3 sides
Line segments are sides
Sides meet is call a vertex
More Polygon Terms
Diagonal – connects two non consecutive
vertices
Concave – at least one diagonal outside polygon,
dented in
Convex – no diagonals outside polygon
Perimeter – distance around polygon
Area – space polygon covers up
Define these types of Polygons pg 56
Equilateral
All the sides of the polygon are
congruent
Equiangular
All the interior angles of the
polygon are congruent
Regular
All sides are congruent and all
angles are congruent
Types and prop of polygons
name
Triangles
Triangles
Quadrilater
Quadrilateral
al
Pentagon
Pentagon
Hexagon
Hexagon
Heptagon
Heptagon
Octagon
Octagon
Nonagon
Nonagon
Decagon
Decagon
Undecagon
Undecagon
Dodecagon
Dodecagon
N-agon
N-agon
name
sum of
measure of each sum of
measure of each
interior interior angle if exterior exterior angle if a number of
sum of
measure of each interior
sum of
measure of each exterior
number of
angles
regular
polygon
anglesangles angle
regular
poygon
diagonals
interior
angles angle
if regular
polygon
exterior
if a regular
poygon
diagonals
sides
sides
N
3
180
60
360
120
0
4
360
90
360
90
2
5
540
108
360
72
5
6
720
120
360
60
9
7
900
128.5714286
360
51.42857143
14
8
1080
135
360
45
20
9
1260
140
360
40
27
10
1440
144
360
36
35
11
1620
147.2727273
360
32.72727273
44
12
1800
150
360
30
54
180(n-3)
sum/n
360 360/n
n(n-3)/2
Triangles – define the following pg 60
Right
Has only one right angle
In some case why can it have
only one of that type of angle?
Acute
All 3 angles are acute angles
Triangles interior angles add up
to 180 and has 3 angles, if it
had 2 right angles it is already
at 180 and if it had 2 obtuse
angles it would be over 180
Obtuse
Has only one obtuse angle
Notice the names of all these triangles deal with the type(s) of angle the
triangle has
More triangles pg 61
Scalene
No sides congruent
Isosceles
2 congruent sides, also has two
congruent base angles
Equilateral
All sides are congruent
Notice all these triangles are named based on sides congruent
When naming a triangle you need to use both the name for type of angle and
number of congruent sides
Classify vs Naming
Classify is what we use the angles and sides for
Naming we use the vertices of the triangle
Naming Polygons you need to go in order of
vertices – either clockwise or counter clockwise,
you can not skip over a vertex
Consecutive vertices means one right after the
other
Congruent Polygons
Polygons can be congruent but corresponding
parts need to be congruent
Corresponding – same location in the two
polygons
Congruent angles and sides
Congruency Statement – name the polygons
congruent in the correct order of congruent
vertices
Examples
Naming and Congruency Statements
Quadrilaterals define and list
properties pg 64
Parallelogram
Rectangle
2 pairs of parallel sides
Opposite sides congruent
Opposite angles congruent
Consecutive angles supplementary
Diagonals
All properties of a parallelogram and
All angles 90 degrees
Rhombus
All properties of a parallelogram and all
sides congruent
Square
All properties of a parallelogram and all
sides congruent and all angles 90
degrees
Trapezoid
1 pair of parallel sides, there are 3 types we will
discuss later
Kite
2 pairs of congruent consecutive sides, 1 pair of
congruent angles
Quadrilaterals
We will go into more depth with these shapes
and come up with some additional properties as
well
Homework
Due by end of class
Wkst Aliens
Wkst Airlines
In your notes
Pg 57 15,16,17
Pg 63 15 and 16
Pg 66 9 and 10