A square is a quadrilateral because it satisfies the basic definition of a quadrilateral: it has four sides, four vertices (corners), and its sides form a closed shape.

1. What is a quadrilateral?

  • A quadrilateral is a polygon (flat, closed shape) with:
    • 4 sides
    • 4 angles
    • 4 vertices (corners)
  • The interior angles of any quadrilateral add up to 360 degrees.

2. What is a square?

  • A square is a special kind of quadrilateral where:
    • All 4 sides are equal in length.
    • All 4 angles are right angles (90 degrees).
    • Opposite sides are parallel.
  • Because it is a quadrilateral with extra properties (equal sides and right angles), it’s sometimes called a “regular” quadrilateral.

3. So why is a square a quadrilateral?

To explain it step by step:

  1. Draw a square ABCD.
  2. Count the sides: AB, BC, CD, DA → there are 4 sides.
  3. Count the corners: A, B, C, D → there are 4 vertices.
  4. The sides join end to end and come back to the starting point, so it forms a closed shape.

Since a quadrilateral is any closed shape with four sides and four vertices, and a square clearly has four sides and four vertices, a square fits the definition of a quadrilateral.

In short:
Every square is a quadrilateral, but not every quadrilateral is a square.

4. Mini “story” to remember

Imagine a big family called “Quadrilaterals.” The only rule to join this family is:
“Have exactly four sides and be a closed shape.”

  • Rectangles, rhombuses, trapeziums, kites – they all get in as long as they follow the four-sides rule.
  • A square not only follows the family rule (four sides) but also brings extra neatness: all sides equal, all angles 90°. So it’s like the very well-organized cousin in the quadrilateral family.

5. One-line answer for exams

  • “A square is a quadrilateral because it is a closed plane figure with four sides and four vertices, which is exactly the definition of a quadrilateral.”

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