What it does
A quadrilateral is any shape with four straight sides. The special ones (square, rectangle, rhombus, parallelogram, kite and trapezium) are told apart by a handful of facts: which sides are parallel, which are equal, which angles are right angles, and how the diagonals behave.
This page puts a quadrilateral ABCD on a square grid. Drag any corner, or type its coordinates, and it shows at once:
- the four sides (as exact square roots where needed),
- the four angles, which always add to 360°, even when the shape is concave and one angle is more than 180°,
- how many pairs of sides are parallel,
- the diagonals: their lengths, whether they cut each other in half, and whether they cross at 90°,
- the area, and the family name.
Under the name, a row of family labels lights up for every family the shape belongs to. A square lights up as a rectangle, a rhombus, a parallelogram, a kite and a trapezium too, which is the idea behind the “family tree” of quadrilaterals. If two sides cross like a bow tie, the page says it is not a quadrilateral at all.
It follows the Class 8 chapter Understanding quadrilaterals and the Class 9 chapter Quadrilaterals (the angle sum, the parallelogram theorems and the midpoint theorem).
To draw these shapes with ruler and compass, use interactive geometry construction. Diagonals and right angles lead straight to pythagoras proof playground, and a quadrilateral split by a diagonal into two triangles can be measured with heron's formula explorer.
How to use it
- Pick a starting shape, such as Parallelogram or Kite.
- Drag A, B, C or D. Corners snap to whole grid points, so lengths and areas stay exact.
- Or type x and y for each corner in the boxes under the picture.
- Tick Diagonals to draw AC and BD, and Join the midpoints to see the midpoint parallelogram.
- Read the name, the lit-up families and the list of facts.
A worked example
The page starts with A(1, 1), B(7, 1), C(9, 4) and D(3, 4).
- AB and DC are both 6 units long and horizontal; BC and AD both go 2 across and 3 up, so they are parallel and equal (√13 ≈ 3.61). Both pairs of opposite sides are parallel: a parallelogram.
- ∠A = ∠C ≈ 56.3° and ∠B = ∠D ≈ 123.7°. Opposite angles are equal, next-door angles add to 180°, and all four add to 360°.
- The diagonals AC and BD both have their midpoint at (5, 2.5), so they cut each other in half.
- Area = base × height = 6 × 3 = 18 square units.
Drag C to (7, 4) and D to (1, 4): every angle becomes 90° and the name changes to rectangle, while parallelogram stays lit.
Tips
- In a concave quadrilateral (a dart), one diagonal lies outside the shape.
- Some books say a trapezium has exactly one pair of parallel sides. Here, as in many texts, it means at least one pair, so every parallelogram is also a trapezium.
Check yourself
Four fresh questions each time: the fourth angle from three, the angle next to a given one in a parallelogram, a rhombus side from its diagonals, and angles in a ratio. Nothing is saved.
FAQ
Why do the angles always add to 360°? A diagonal splits the quadrilateral into two triangles, and each triangle’s angles add to 180°.
Is this from the NCERT book? It covers the same topics with fibub’s own examples. fibub is not part of NCERT.
Where the numbers come from
- Angle sum, the properties of special quadrilaterals, the shoelace area formula and the midpoint (Varignon) theorem are standard geometry. Written for fibub.
- Angles and areas checked against a separate Python script (acos of the edge vectors, shoelace area) for a square, rectangle, rhombus, parallelogram, kite, trapezium, isosceles trapezium and a concave dart.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.