Home › Math Adventures › Geometry› Quadrilaterals
← Back to Math Adventures

Quadrilaterals

Overview

The family of four.

What is it?

Polygons with exactly four sides and four vertices.

History

The basis of land division and city blocks.

Key Idea

A Square is a Rectangle, but a Rectangle isn't always a Square.

Practice This Topic

Concept Guide

Plain English: This is a family tree. The 'Quad' family includes messy shapes. The 'Parallelogram' cousins have parallel sides. The 'Rectangle' kids have straight corners. The 'Square' is the perfect child that has it all.

Real-world example: Screens (16:9 Rectangles). Paper (A4 Rectangles). Kites.

How to do it

  1. Check parallel sides. (2 pairs = Parallelogram).
  2. Check corners. (4 Right angles = Rectangle).
  3. Check side lengths. (4 Equal sides = Rhombus).
  4. If it has ALL of these, it is a Square.
⚠

Common Pitfall

Thinking a Rhombus (diamond) is a Square. A Rhombus has equal sides, but doesn't need 90-degree angles.

Word Problem
"A shape has 4 equal sides but no right angles. What is it?"
Reasoning: Equal sides means Rhombus. No right angles means it is NOT a square. Answer: Rhombus.

Practice Examples

Hierarchy
Quad | Parallel / \ Rect Rhomb \ / Square
Square inherits all traits.