📐 Classification of Quadrilaterals
Written By: Ujjwal Matoliya
(Types based on Sides, Angles, and Diagonals)
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| Classification of Quadrilaterals – Educational Math Chart (Credit: Ujjwal Matoliya) |
🔷 1️⃣ Parallelogram
✅ Properties:
Sides: Opposite sides are equal and parallel.
Angles: Opposite angles are equal. Adjacent angles are supplementary (sum = 180°).
Diagonals: Diagonals bisect each other.
✏ Explanation:
A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel. Because of this, opposite sides are equal in length. If one angle is 60°, the adjacent angle will be 120°. The diagonals cut each other into two equal halves.
🔷 2️⃣ Rectangle
✅ Properties:
Sides: Opposite sides are equal and parallel.
Angles: All angles are 90°.
Diagonals: Diagonals are equal and bisect each other.
✏ Explanation:
A rectangle is a special type of parallelogram where all angles are right angles. Because all angles are 90°, it forms a perfect rectangular shape. The diagonals are equal in length.
🔷 3️⃣ Square
✅ Properties:
Sides: All four sides are equal and parallel in pairs.
Angles: All angles are 90°.
Diagonals: Diagonals are equal, bisect each other, and are perpendicular.
✏ Explanation:
A square is both a rectangle and a rhombus. It has all equal sides and all right angles. Its diagonals cross at 90° and divide each other equally.
🔷 4️⃣ Rhombus
✅ Properties:
Sides: All sides are equal.
Angles: Opposite angles are equal.
Diagonals: Diagonals bisect each other at right angles.
✏ Explanation:
A rhombus looks like a tilted square. All sides are equal, but angles are not necessarily 90°. Its diagonals cross each other at right angles.
🔷 5️⃣ Trapezium (Trapezoid)
✅ Properties:
Sides: Only one pair of opposite sides is parallel.
Angles: Adjacent angles along the non-parallel sides are supplementary.
Diagonals: Diagonals are generally not equal (except in isosceles trapezium).
✏ Explanation:
A trapezium has only one pair of parallel sides. The other two sides are not parallel. If the non-parallel sides are equal, it is called an isosceles trapezium.
📊 Summary Chart
| Quadrilateral | Sides | Angles | Diagonals |
|---|---|---|---|
| Parallelogram | Opposite sides equal & parallel | Opposite angles equal | Bisect each other |
| Rectangle | Opposite sides equal | All 90° | Equal & bisect |
| Square | All sides equal | All 90° | Equal, bisect & perpendicular |
| Rhombus | All sides equal | Opposite angles equal | Perpendicular bisectors |
| Trapezium | One pair parallel | Not all equal | Not equal generally |