Section 3.1 – Symmetry in Polygons

Polygon – a plane figure formed from 3 or more segments such that each segment intersects exactly two other segments, one at each endpoint, and no two segments with a common endpoint are collinear. The segments are called the sides of the polygon and the common endpoints are called the vertices of the polygon.

Polygons Not Polygons

Polygons Classified by Number of Sides

Triangle 3	Nonagon 9
Quadrilateral 4	Decagon 10
Pentagon 5	11-gon 11
Hexagon 6	Dodecagon 12
Heptagon 7	13-gon 13
Octagon 8	n-gon n

Equilateral polygon – a polygon in which all sides are congruent

Equiangular polygon – a polygon in which all angles are congruent

Regular polygon – a polygon that is both equilateral and equiangular

Center of a regular polygon – the point that is equidistant from all vertices of the polygon

Central angle – an angle whose vertex is the center of the polygon

Symmetry

Reflectional Symmetry – a figure has reflectional symmetry if and only if its reflected image across a line coincides exactly with its preimage. This line is called an axis of symmetry.

Rotational Symmetry – a figure has rotational symmetry if and only if it has at least one rotation image, not counting rotation images of 0° or multiples of 360°, that coincides with the original image.

Classifying Triangles by Sides

Equilateral Triangle – 3 congruent sides

Isosceles Triangle – at least 2 congruent sides

Scalene Triangle – no sides congruent