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Class 8 Quadrilaterals: cheat sheet
CBSE Mathematics. The angle sum of a quadrilateral, and the sides, angles and diagonals of parallelograms, rectangles, rhombuses, squares, trapeziums and kites.
Key ideas
- The angles of any quadrilateral add up to 360°.
- Parallelogram: opposite sides parallel and equal, opposite angles equal, neighbouring angles add to 180°, diagonals bisect each other.
- Rectangle: a parallelogram with right angles; its diagonals are equal.
- Rhombus: all sides equal; its diagonals bisect each other at right angles and bisect its angles.
- Square: a rectangle and a rhombus at once; its diagonals are equal, perpendicular and make 45° with the sides.
- Trapezium: exactly one pair of parallel sides. Kite: two pairs of equal neighbouring sides, diagonals at right angles.
Remember
| Angle sum | ∠A + ∠B + ∠C + ∠D = 360° |
| Parallelogram | ∠A = ∠C, ∠B = ∠D, ∠A + ∠B = 180° |
| Rhombus diagonals | half-diagonals and a side form a right triangle |
Watch out
- Saying a rhombus has equal diagonals (only a square does).
- Taking all angles of a parallelogram as 90°.
- Calling every quadrilateral with perpendicular diagonals a rhombus (a kite has them too).
Worked example
In square PQRS of side 10 cm, the diagonals meet at O. Find ∠POQ, ∠OPQ and the perimeter.
Working: the diagonals of a square are perpendicular and bisect its 90° angles
Answer: 90°, 45°, 40 cm
Practise Quadrilaterals
Revise with this page, then practise: every Quadrilaterals sheet in the app is new, with an answer key and working.
Coming soon for Android and iPhone.