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Quadrilaterals

Explore the properties of four key quadrilaterals interactively — sides, angles, diagonals, and their hierarchy.

What is a Quadrilateral?

A quadrilateral is a closed polygon with exactly four sides, four angles, and four vertices. The sum of interior angles of any quadrilateral is always 360°.

Interactive Explorer

Drag the vertices to reshape the figure freely. Then use the Lock Constraints buttons to force geometric conditions — watch which properties light up as you tighten the constraints.

How to Use This Explorer

  1. Free drag — move any vertex. Notice the shape stays a general quadrilateral.
  2. Lock ∥∥ Parallelogram — both pairs of opposite sides stay parallel as you drag.
  3. Add ∟ Right angles — it becomes a Rectangle. Drag to see it stay rectangular.
  4. Add = Equal sides on top of right angles — it collapses into a Square.
  5. Try Trapezium instead — only one pair of parallel sides. Notice how fewer properties light up.

The Hierarchy

A Square is the most constrained shape — it satisfies ALL properties simultaneously.

Parallelogram
├── Rectangle  (+ right angles)
│     └── Square  (+ equal sides)
└── Rhombus    (+ equal sides)
      └── Square  (+ right angles)

Key Properties at a Glance

PropertyParallelogramRectangleRhombusSquareTrapezium
Opposite sides equal✓✓✓✓✗
All sides equal✗✗✓✓✗
All angles = 90°✗✓✗✓✗
Diagonals equal✗✓✗✓✗
Diagonals bisect each other✓✓✓✓✗
Diagonals perpendicular✗✗✓✓✗
Lines of symmetry02241

Area Formulas

ShapeFormula
Squarea2a^2
Rectanglel×bl \times b
Rhombus12d1d2\dfrac{1}{2} d_1 d_2
Parallelogramb×hb \times h
Trapezium12(a+b)×h\dfrac{1}{2}(a+b) \times h

Practice Problems

  1. A rhombus has diagonals 16 cm and 12 cm. Find its area and side length.
  2. The diagonal of a square is 10210\sqrt{2} cm. Find its side and area.
  3. In a parallelogram ABCD, ∠A = 70°. Find all four angles.
  4. Prove that the diagonals of a rectangle are equal.
  5. (JEE level) ABCD is a parallelogram. P is the midpoint of BC. Prove that DP trisects diagonal AC.