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

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:

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

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

Answers:

1. A polygon with seven sides is called a heptagon.
2. A quadrilateral with all its sides equal but not all angles being right angles is a rhombus.
3. 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.