The term POLYGON means "many-angled" (Poly = many) & (Gon = angles) By definition A Polygon is: a closed figure formed by a finite number of coplanar.
Dec 17, 2015
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The term POLYGON means "many-angled" (Poly = many) & (Gon = angles)
By definition A Polygon is:•a closed figure formed by a finite number of coplanar segments such that •the sides that have a common endpoint are noncollinear and •each side intersects exactly two other sides, but only at their endpoints
Wow that is pretty technical...... does that make sense to you?.... basically a polygon is a closed shape that is made up of line segments (no curves) and of
course sides can only touch at the endpoints...... Does that make more sense?
POLYGONS Non Polygons
A polygon is a closed plane figure bounded by straight line segments. The line segments are
called the sides of the polygon, and the points at which they intersect are called vertices. A polygon has the same number of sides as it has vertices.
Polygons are classified according to the number of sides they have.
What is a three-sided polygon called?
What is a four-sided polygon called?
If all the sides and all the angles of a polygon are congruent the polygon is said to be regular.
What kind of triangle is regular?
What kind of quadrilateral is regular?
Equilateral triangle
square pentagon hexagon
heptagon octagon nonagon decagon
A polygon that is not regular is irregular.
A concave polygon is 'caved' in - some of its sides are bent inward. For example the red and green shape are both concave polygons.
An easy way to determine whether a shape is concave or not is the SEGMENT TEST. If you can draw a straight segment between two points in the shape but part of the segment leaves the shape then the shape is concave.
A convex polygon is the opposite of concave - when the segment test fails for all segments in the shape. A more formal way of defining convex is a polygon such that no line containing a side of the polygon contains a point in the interior of the polygon.
1.2.
3.4.
5.
6.
A diagonal is a segment drawn from one vertex to another that is not a side.
Some diagonals:
All of the diagonals in a convex polygon will lie inside the polygon.At least one diagonal in a concave polygon will lie outside of the polygon.
The interior angles in a polygon are formed by the sides.
Interior angle
The number of interior angles is equal to the number of sides and number of vertices in the polygon.
The sum of the measures of the interior angles in a triangle is ____________.
The sum of the measures of the interior angles in a convex quadrilateral is _____________.
Polygon
name
Number of sides
# of diagonals drawn from one vertex
# of triangles formed
Sum of measures of
interior angles
triangle
quadrilateral
5
6
7
8
9
n
3
4
0
1
1 180
2 360
pentagon 2 3 540
n = number of sides
Exterior angles are formed by extending a side of the polygon.
exterior angle
exterior angle
exterio
r angle
exterior angle
(that means one exterior angle at each vertex)
60° 60°
60°
120°
120°
120°
Sum of exterior angles =
TRIANGLE
Sum of exterior angles =
95°95°
120°120°
110°
Sum of exterior angles =
QUADRILATERAL PENTAGON
QUIZ
Definitions / examples
Geometry home page
Venn diagrams
Polygon definitionRegular / irregular
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