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Asked: 2026-10-03T06:00:52+00:00 In:

The diagonals AC and BD of a parallelogram ABCD intersect at O. A line through O meets AB and CD at points P and Q respectively. Show that O is the midpoint of PQ. (Multiple proofs are possible. Which is the simplest?)

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In triangle OBP and triangle ODQ, OB = OD, ∠POB = ∠QOD and alternate interior angles ∠OBP = ∠ODQ. By ASA congruence, triangle OBP ≅ triangle ODQ, proving OP = OQ; this direct triangle congruence is simplest.

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

cbse released class 9 ganita manjari part 2 bookchapter 12 quadrilaterals (ganita manjari 2) solutionsdiagonals ac and bd of a parallelogram abcdganita manjari part 2 chapter 12 quadrilaterals solutionsganita manjari part 2 solutions available!show that o is the midpoint of pq
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    1. Diagonals of parallelogram ABCD bisect each other, giving OB = OD. Since AB ∥ CD, alternate interior angles yield ∠PBO = ∠QDO. Furthermore, ∠POB = ∠QOD as vertically opposite angles. Therefore, triangle POB ≅ triangle QOD by ASA congruence. Corresponding sides give OP = OQ, meaning O is the midpoint of PQ. This standard ASA congruence proof is the simplest approach.

       

      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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