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Kiara Singh
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Asked: 2026-10-01T06:12:18+00:00 In:

Suppose the midpoints of sides AB, BC, CD and DA of a quadrilateral ABCD are P, Q, R and S respectively. (i) Show that PR and QS bisect each other. (ii) Show that if AC = BD, then PR and QS are perpendicular. Is the converse true?

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(i) By Varignon’s Theorem, PQRS is a parallelogram, so its diagonals PR and QS bisect each other.

(ii) PQ = RS = AC/2 and QR = SP = BD/2. If AC = BD, PQRS is a rhombus, having perpendicular diagonals. Yes, the converse is true.

Cbse released Class 9 Ganita Manjari Part 2 book
Class 9 Chapter 12 Quadrilaterals (Ganita Manjari 2) Solutions

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    1. (i) By the Midpoint Theorem, PQ ∥ AC ∥ SR and PS ∥ BD ∥ QR, meaning PQRS is a parallelogram whose diagonals PR and QS bisect each other.

      (ii) Since PQ = AC/2 and QR = BD/2, if AC = BD, all sides of PQRS are equal, making it a rhombus whose diagonals are perpendicular. The converse is true: perpendicular diagonals in parallelogram PQRS make it a rhombus, which forces AC = BD.

       

      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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