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Piyush365
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Asked: 2026-10-05T07:29:33+00:00 In:

Complete the following proof of the Midpoint Theorem. Extend segment PQ beyond Q until point S. By how much should we extend PQ? It would be good to be able to prove that △APQ ≅ △CSQ. (Why?) Use this as a guide to specify the location of S and then complete this proof. (ii) Give a similar proof of the converse of the Midpoint Theorem (Theorem 7). Start by extending PQ up to a suitable point S.

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Extend PQ so QS = PQ. By SAS, △APQ ≅ △CSQ, making CS = AP = PB and CS ∥ PB. Thus PBCS is a parallelogram, giving PQ ∥ BC and PQ = BC/2. For (ii), complete PBCS similarly to prove Q bisects AC.

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

complete the following proof of the midpoint theoremganita manjari part 2 chapter 12 quadrilaterals solutionsganita manjari part 2 chapter 12 question answerquadrilaterals solutions – ganita manjari part ii chapter 12similar proof of the converse of the midpoint theorem (theorem 7)use this as a guide to specify the location of s
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    1. (i) Extend PQ to S such that QS = PQ. Since AQ = CQ and vertical angles match, △APQ ≅ △CSQ by SAS. This gives CS = AP = PB and alternate interior angles show CS ∥ PB. Hence PBCS is a parallelogram. Therefore PQ ∥ BC and PQ = PS/2 = BC/2. (ii) Through C draw a line parallel to AB meeting extended PQ at S, forming parallelogram PBCS with CS = PB = AP. Then △APQ ≅ △CSQ by AAS, which proves AQ = QC.

       

      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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