Discover the Key Properties and Characteristics of Regular Polygons: Equal Sides, Angles, Symmetry, and Diagonals

regular polygon

A regular polygon is a polygon (a closed plane figure with straight sides) in which all the sides are of equal length and all the angles are of equal measure

A regular polygon is a polygon (a closed plane figure with straight sides) in which all the sides are of equal length and all the angles are of equal measure. Some examples of regular polygons include equilateral triangle, square, pentagon, hexagon, octagon, etc.

Here are some key properties of regular polygons:

1. Equal side lengths: In a regular polygon, all the sides have the same length. For example, in an equilateral triangle, all three sides are equal.

2. Equal interior angles: In a regular polygon, all the interior angles have the same measure. The measure of each interior angle can be found using the formula: (n-2) × 180° / n, where n is the number of sides in the polygon. For example, in a regular pentagon, each interior angle measures (5-2) × 180° / 5 = 108°.

3. Equal exterior angles: In a regular polygon, all the exterior angles have the same measure. Each exterior angle can be found by subtracting the interior angle from 180°. For example, in a regular hexagon, each interior angle measures 120°, so each exterior angle measures 180° – 120° = 60°.

4. Symmetry: Regular polygons exhibit rotational symmetry, meaning they can be rotated by certain angles and still look the same. For example, a square can be rotated by 90° and still appear unchanged.

5. Diagonals: Diagonals are the line segments connecting two non-adjacent vertices of a polygon. In a regular polygon, the number of diagonals can be found using the formula: n × (n-3) / 2, where n is the number of sides in the polygon. For example, in a regular hexagon, there are 9 diagonals [(6 × (6-3)) / 2].

These are some of the key characteristics of regular polygons. Remember that regular polygons have uniform side lengths and angles, making them distinct from irregular polygons.

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