Revision Notes: Class 8 Maths Chapter 4 Quadrilaterals

Class 8 Maths Chapter 4: Quadrilaterals — Quick Revision Notes

• Angle Sum Property: the four interior angles of any simple quadrilateral always sum to 360° — proved by splitting it into two triangles with a diagonal.
• Rectangle: all angles 90°, opposite sides equal; diagonals are equal and bisect each other (not necessarily perpendicular).
• Square: a rectangle with all sides equal; diagonals are equal, bisect each other, are perpendicular, and bisect the vertex angles (each 90° corner splits into two 45° angles).
• Parallelogram: both pairs of opposite sides parallel; any ONE of these is sufficient to prove it: opposite sides equal, opposite angles equal, or diagonals bisect each other.
• Rhombus: a parallelogram with all four sides equal; diagonals are perpendicular bisectors of each other and bisect the vertex angles, but aren’t necessarily equal.
• Kite: two distinct pairs of adjacent equal sides; one diagonal is the perpendicular bisector of the other, but diagonals are unequal and it’s generally not a parallelogram.
• Trapezium: exactly one pair of parallel sides; co-interior angles on the parallel sides sum to 180°. An isosceles trapezium has equal legs and equal base angles but is NOT a parallelogram.
• Family hierarchy: square ⊂ rectangle ⊂ parallelogram; square ⊂ rhombus ⊂ kite; parallelogram ∩ kite = rhombus; rectangle and kite never overlap (except the trivial square case).
• Proof method: most properties are proved using triangle congruence (SSS, SAS, ASA) after drawing a diagonal — measurement alone only suggests a conjecture, not a proof.
• Common traps: perpendicular diagonals alone do NOT guarantee a rhombus (a kite also has them); equal bisecting diagonals give a rectangle, not necessarily a square.

Written by Satish

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