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Asked: 2026-09-30T07:13:00+00:00 In:

Let ABCD be a parallelogram with AB ≠ BC. Show that the pairwise intersection points of the four angle bisectors form the vertices of a rectangle (see Fig. 12.11). Why did we assume AB ≠ BC?

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Adjacent angles of a parallelogram sum to 180°, so their bisectors add to 90°, forcing right angles at intersections to form a rectangle. If AB = BC, all bisectors intersect at a single point.

Cbse Class 9 Maths Ganita Manjari Part 2 Solutions
class 9 maths ganita manjari part 2 chapter 12 question answer

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    1. Adjacent angles of parallelogram ABCD are supplementary, summing to 180°. In triangles formed by adjacent bisectors, half-angles sum to 90°, forcing each intersection angle to be 90°. As all four interior angles equal 90°, the figure PQRS is a rectangle. We assume AB ≠ BC because if AB = BC (a rhombus), the angle bisectors are the diagonals, which concur at one point rather than forming a quadrilateral.

       

      For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 12 Quadrilaterals Question Answer (2026-27)

      https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-12/

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