complete the following proof of the midpoint theorem – Discussion Forum

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Piyush365

Asked: October 5, 2026In: Class 9 Maths

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.

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 ...