Quadrilaterals — Class 8 Mathematics

This chapter studies four-sided figures and proves their properties through geometric reasoning rather than measurement alone. Starting from the Carpenter’s Problem of joining two strips to make a rectangle, it deduces that the diagonals of a rectangle are equal and bisect each other, and that a quadrilateral with all four angles must be a rectangle. A square is a special rectangle with all sides equal; its diagonals are equal, bisect each other at , and bisect its angles. A central result is that the angle sum of any quadrilateral is , found by splitting it into two triangles. Relaxing conditions builds a family of quadrilaterals: a parallelogram has both pairs of opposite sides parallel (opposite sides and angles equal, diagonals bisecting each other); a rhombus has all sides equal, with diagonals that bisect each other at right angles and bisect the angles; a kite has two adjacent pairs of equal sides; and a trapezium has at least one pair of parallel sides, with the isosceles trapezium having equal base angles. Venn diagrams capture how squares, rectangles, rhombuses and parallelograms are nested.