POLYGONS
1. What makes a polygon?
a. Must have 3 or more straight lines
b. Must be closed, all the lines connect at a point.
c. Must never have curves
d. Must never have intersecting lines.
e. Is a 2-dimensional shape.
Not a Polygon
(has a curve)
Polygon
(straight sides)
Not a Polygon
(open, not closed)
2. Types of Polygons
a. Regular Polygons: all sides are of equal length (all angles are congruent).
b. Irregular Polygons: different measures for side lengths or angles.
Regular
Irregular
3. Concave or Convex
a. A convex polygon has no angles pointing inwards. More precisely, no internal angle can be
more than 180˚.
b. A concave angle has an internal angle greater than 180˚. (THINK: concave has a “cave” in,
one of the sides “caved in” itself.)
Convex
Concave
4. Simple or Complex
a. A simple polygon has only one boundary, and it doesn’t cross over itself.
b. A complex polygon intersects itself! Many rules about polygons don’t work when it is
complex.
Simple Polygon
(this one's a
Pentagon)
Concave Octagon
Complex Polygon
Irregular
Hexagon
Complex
Polygon
(a "star
polygon")
Important Helpful Hints:
Tic Marks and Arc Marks
1. Tic Marks show sides are congruent.
2. Arc Marks shows angles are congruent.
Equal or Congruent
1. Congruent ≅, use when talking or writing about things such as angles, polygons, shapes, segments,
lines, rays
2. Equal = is used only when we talk about measures and numbers
3. Examples: ∠1 ≅ ∠2, AB ≅ XY, m∠1 = m∠2, (means the measure of angle 1 is equal to the
measure of angle 2). mAB = mXY , (means the measure of segment AB is equal to the measure of
XY).
Names of Polygons
NAMES of POLYGONS
Number of Sides
3
4
5
6
7
8
9
10
n
x
15
57
143
Name of Polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
n-agon
x-agon
15-agon
57-agon
143-agon
4. Sum of Interior Angles (Regular Polygons): Adding up all the angles inside the polygon.
a. (n - 2)180 = total sum
b. Example: 15 a-gon sum of interior angles is (15-2)180, (13)180 = 2340˚.
5. Single Angle Measurement in a polygon.
a. Find the Sum of the Interior Angles
b. Divide by the number of sides the polygon has
2340
c. Example: 15 a-gon sum of Interior is 2340˚ now divide by 15 15 = 156˚
6. Exterior Angles of all POLYGONS is always 360˚.
a. Take the single angle if you already know it and the exterior angle is supplementary.
360
b. Take 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑖𝑑𝑒𝑠
c. Example for the 15 a-gon
360
15
= 24˚ 𝑜𝑟 180 − 156 = 24˚
7. Polygon Parts
a. Side: one of the line segments that make up the polygon
b. Vertex: point where two sides meet.
c. Diagonal: A line connecting two vertices that isn’t a side. A line connecting two nonconsecutive angles.
d. Interior Angle: An angle formed by two adjacent sides inside the polygon. There will be as
many angles as there are the numbers of sides of the polygon.
e. Exterior angle: Supplementary Angle to an interior angle. There will be as many exterior
angles as there are the numbers of sides of the polygon.