Quadrilaterals

About this chapter

Quadrilaterals is a Class 8 mathematics chapter. The word 'quadrilateral' comes from the Latin quadri (four) and latus (sides) — a closed four-sided figure whose angles lie between its sides. The chapter develops six big ideas through ten deductions and many constructions. It opens with the Carpenter's Problem — two wooden strips of equal length joined at midpoints form a rectangle — which gives a second, equivalent definition of a rectangle: a quadrilateral whose diagonals are equal and bisect each other. The argument uses SAS, SSS and AAS congruence on the triangles formed by the diagonals. The same Carpenter's Problem extended to perpendicular diagonals gives the square. It proves that the sum of all four angles of any quadrilateral is 360°, by drawing one diagonal and using the triangle-angle sum 180°. It introduces the parallelogram (opposite sides parallel), proves opposite angles are equal and diagonals bisect each other. It builds the rhombus (all four sides equal) and shows its diagonals bisect each other at 90° and bisect its angles. It brings in the kite (two pairs of adjacent equal sides) and the trapezium (at least one pair of parallel sides, isosceles when the non-parallel sides are equal). The chapter closes with the famous Venn-diagram hierarchy — every square is a rectangle, a rhombus and a parallelogram; every rectangle and every rhombus is a parallelogram; every parallelogram is a trapezium. CTET Paper 2 tests this chapter through property-recall items, angle-sum word problems, true/false statements about diagonals, and pedagogy items on conjecture-versus-proof and the Venn classification.