Lesson's Content
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Lesson's Glossary
Angle
Geometry shape formed by two rays (initial and ending sides of the angle) that share a common endpoint called the vertex. You may name an angle using the vertex, or a point in each ray and the vertex label in the center.
Concave polygon
If a polygon has diagonals that lie outside the polygon then the polygon is concave.
Convex polygon
A convex polygon is any polygon that is not concave.
Decagon
A ten-sided polygon.
Dodecagon
A twelve-sided polygon.
Heptagon
A seven-sided polygon.
Hexagon
A six-sided polygon.
irregular polygon
An irregular polygon is any polygon that is not regular.
N-gon
A polygon with n sides.
Nonagon
A nine-sided polygon.
Octagon
An eight-sided polygon.
Pentadecagon
A 15-sided polygon.
Pentagon
A five-sided polygon.
Polygon
A polygon is a two-dimensional geometric figure with these characteristics: •
It is made of straight line segments.
Each segment touches exactly two other segments, one at each of its endpoints.
It is closed -- it divides the plane into two distinct regions, one inside and the other outside the polygon.
Regular polygon
A regular polygon has sides that are all the same length and angles that are all the same size.
Quadrilateral
A four-sided polygon.
Septagon
A seven-sided polygon.
Side of a polygon
- a single segment from the union that forms a polygon.
Vertex of a polygon
An endpoint of a segment in a polygon.
Interactive Geometric Applets: Relevant Theorems.
In this lesson you will be given the proof for Interior Angle Sum Theorem.
This states that the sum of the interior angles in a convex polygon is
the number of sides decreased in two units times 180°.
This applet highlights this relationship by drawing as many diagonals as possible
from a given vertex, and adding the sum of the interior angles; this is equal to
multiply the interior angle sum of a triangle by the number of triangles that
you get upon drawing the diagonals as indicated.
The resolution for this applet is 1200x600
The sum of the interior angles of a convex polygon changes with the number of sides;
while the sum of the exterior angles is always 360°.
This applet compares and contrast this fact by presenting an irregular pentagon
next to a triangle, and showing both angle sums.
The exterior angle sum of a convex polygon is always 360°, and as stated above the sum
of the interior angles changes with the type of polygon. What about regular vs irregular
polygon? This applet gives answer to that question.
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