Symmetry in Polygons

1
Chapter 3.1

• Symmetry in Polygons

2
Definition of a Polygon
Definition of a polygon

• A plane figure formed from three or more segments
  such that each segment intersect exactly two
  other segments, one at each endpoint,and no two
  segment with a common end point are collinear
• The segments are called the side of the polygon
• The common endpoints are called the vertices of
  the polygon
• A rectangle is an example if polygon

3
Convex and Concave Polygons

• A polygon in which any line segment connecting
  two points of the polygon has no part outside the
  polygon
• A polygon that is not convex
• An example of a convex polygon is a square
• An example of a concave polygon is a star

4
Triangle Classifications

• Three congruent sides equilateral
• At least two congruent sides isosceles
• No congruent sides scalene

5
Polygon Classifications

• Triangle 3 sides
• Quadrilateral 4 sides
• Pentagon 5 sides
• Hexagon 6 sides
• Heptagon 7 sides
• Octagon 8 sides

• Nonagon 9 sides
• Decagon 10 sides
• 11-gon 11 sides
• Dodecagon 12 sides
• 13-gon 13 sides
• N-gon n sides

6
No Symmetry

• No symmetry is where the object is not able to be
  reflected or rotated so therefore there is not
  symmetry
• The following figure has no symmetry

7
Axes of Symmetry

• Axis of symmetry is the line on a reflected image
  that coincides exactly with the preimage
• The line through the heart shows the axis of
  symmetry

8
Reflectional Symmetry

• A figure has reflectional symmetry if and only if
  its reflected image across a line coincides
  exactly with the preimage

9
Rotational Symmetry

• A figure has rotational symmetry if and only if
  it has at least one rotational image, not
  counting rotation images of 0 degrees or 360
  degrees that coincides with the original image