A polygon is defined as a plane figure formed by three or more line segments that intersect only at their endpoints. It must be a closed region. Regular polygons have equal side lengths and equal interior angles, while equilateral polygons only have equal side lengths. Convex polygons are those where any segment joining two interior points lies entirely within the polygon, while concave polygons contain at least one interior angle greater than 180 degrees.
3. What is a polygon?
• A polygon is a plane figure.
• A polygon is a closed region.
• A polygon is formed by three or more
segments as its sides.
• Each side of a polygon intersects only
one segment at each of its endpoints.
• poli + gonus “many angled”
19. Parts of a Polygon
• sides
▫ consecutive sides
included angle
▫ nonconsecutive sides
• interior angles / vertex angles
▫ consecutive angles
included side
▫ nonconsecutive angles
• exterior angles
20. Parts of a Polygon
• Diagonals
▫ A diagonal of a polygon is any segment that joins
two nonconsecutive vertices. Figure shows five-
sided polygon QRSTU. Segments QS , SU , UR
, RT and QT are the diagonals in this polygon.
26. Polygon Convexity
A polygonal region is convex if any
segment joining any two points of the
polygon is part of the interior region.
If a polygon is not convex, then its is
concave.
33. Convex or Concave?
Concave
because a segment
connecting points on
the polygon that will
lie in the exterior can
be drawn.
34. A B
D C
Polygons are named by writing their consecutive
vertices in order, such as ABCD or CDAB for the
polygon above.
We cannot name the polygon as DBAC.
35. • Think of words beginning
with the prefixes tri-
, quad-, pent-, and oct-.
• Examples:
triathlon, quadriplegic, pen
tameter, and octopus.
• Meanings? (words and
prefixes)
36. Polygons can be named by their number of sides.
Number of Sides Name of Polygon
3 triangle
4 quadrilateral
5 pentagon
6 hexagon
7 heptagon
8 octagon
9 nonagon
10 decagon
11 undecagon
12 dodecagon
