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Virat
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Asked: 2026-09-30T07:12:57+00:00 In:

The following questions examine converses of true properties. Answer them with Yes or No. If your answer is No, what extra condition can you add so that the answer becomes Yes? (i) If the diagonals of a quadrilateral ABCD bisect its angles, must ABCD be a rhombus? (ii) If the diagonals of a quadrilateral ABCD bisect each other at right angles, must ABCD be a rhombus? (iii) If the diagonals of a quadrilateral ABCD are of equal length, must ABCD be a rectangle?

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(i) Yes.
(ii) Yes.
(iii) No; an isosceles trapezium also has equal diagonals. Extra condition: the quadrilateral must be a parallelogram or its diagonals must also bisect each other.

Ganita Manjari Part 2 chapter 12 question answer
Quadrilaterals Solutions – Ganita Manjari Part II Chapter 12

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    1 Answer

    1. (i) Yes: Diagonals bisecting vertex angles force all opposite sides parallel and adjacent sides equal, creating a rhombus.
      (ii) Yes: Perpendicular bisecting diagonals prove all four sides are congruent through SAS triangle congruences.
      (iii) No: Non-rectangular shapes like isosceles trapeziums have equal diagonals. Extra condition: Add that the diagonals must bisect each other or the quadrilateral must already be a parallelogram.

       

      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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