# How to Classify Polygons: A Step-by-Step Guide to Shape Identification

Polygons are closed, flat (or two-dimensional) shapes formed by straight lines. The term "polygon" comes from the Greek words "poly" (meaning "many") and "gonia" (meaning "angle"). Polygons are primarily classified based on the number of sides they have and their internal angles. This guide will take you through the journey of classifying polygons, providing clarity on their unique characteristics.

## Step-by-step Guide: Classifying Polygons

**Understanding Polygons:**

A polygon is a closed, two-dimensional shape formed by straight line segments. The point where two segments meet is called a vertex, and the segments themselves are the sides.

**Classifying by Number of Sides:**

- riangle (3 sides)
- Quadrilateral (4 sides)
- Pentagon (5 sides)
- Hexagon (6 sides)
- … and so on.

**Classifying by Side Length:**

- Equilateral: All sides are of equal length.
- Isosceles: Two sides are of equal length.
- Scalene: No sides are of equal length.

**Classifying by Interior Angles:**

- Regular Polygon: All interior angles are equal.
- Irregular Polygon: Not all interior angles are equal.

**Special Classifications for Quadrilaterals:**

- Square: All sides equal, and all angles are right angles.
- Rectangle: Opposite sides equal, and all angles are right angles.
- Rhombus: All sides equal, but not all angles are right angles.
- Parallelogram: Opposite sides equal and parallel.
- Trapezoid: Only one pair of opposite sides are parallel.

**Examples**

**Example 1:**

A polygon with five equal sides and five equal angles.

**Solution:**

By the number of sides, it is a **pentagon**.

Since all sides and angles are equal, it is a **regular pentagon**.

**Example 2:**

A polygon with opposite sides equal and one set of parallel sides.

**Solution:**

By the number of sides, it is a **quadrilateral**.

Given its properties, it is classified as a **trapezoid**.

### Practice Questions:

- A polygon has seven sides. What is it called?
- If a quadrilateral has all its sides equal but not all angles are right angles, how would you classify it?
- What differentiates a square from a rhombus?

**Answers:**

- A polygon with seven sides is called a
**heptagon**. - A quadrilateral with all its sides equal but not all angles being right angles is a
**rhombus**. - Both a square and a rhombus have all sides equal. However, a square has all right angles while a rhombus does not necessarily have right angles.

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