Transcript A concave polygon is

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?
Click here to see
some more polygon
names
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
heptagon
square
pentagon
octagon
nonagon
hexagon
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.
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QUIZ
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
triangle
quadrilateral
pentagon
Number of
sides
# of diagonals
drawn from
one vertex
3
0
4
1
5
6
7
8
9
n
2
# of triangles
formed
1
2
3
Sum of
measures of
interior angles
180
360
540
n = number of sides
Exterior angles are formed by extending a
side of the polygon.
exterior angle
exterior angle
(that means one exterior angle at each vertex)
120°
Sum of exterior angles =
60°
TRIANGLE
120° 60°
60°
120°
110°
120°
120°
95° 95°
Sum of exterior angles =
QUADRILATERAL
PENTAGON
Sum of exterior angles =
QUIZ
Definitions / examples
Polygon definition
Regular / irregular
“textbook”
Geometry home page
Venn diagrams
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