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Prove that opposite side mid points joining line segment is parallel to one of the parallel side.?
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Prove that opposite side mid points joining line segment is parallel t...
Given: In triangle ABC, P and Q are mid-points of AB and AC respectively.To Prove: i) PQ || BC ii) PQ = 1 2 BCConstruction: Draw CR || BA to meet PQ produced at R.Proof:∠QAP = ∠QCR (Pair of alternate angles) ---------- (1)AQ = QC (∵ Q is the mid-point of side AC) ---------- (2)∠AQP = ∠CQR (Vertically opposite angles) ---------- (3)Thus, ΔAPQ ≅ ΔCRQ (ASA Congruence rule)PQ = QR (by CPCT) or PQ = 1 2 PR ---------- (4)⇒ AP = CR (by CPCT) ........(5)But, AP = BP (∵ P is the mid-point of the side AB)⇒ BP = CRAlso. BP || CR (by construction)In quadrilateral BCRP, BP = CR and BP || CRTherefore, quadrilateral BCRP is a parallelogram.BC || PR or, BC || PQAlso, PR = BC (∵ BCRP is a parallelogram)⇒ 1 2 PR = 1 2 BC⇒ PQ = 1 2 BC [from (4)]
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Prove that opposite side mid points joining line segment is parallel t...
Sorry my question is incomplete, the question is related to trapezium. But anyway thanks for the answer
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Prove that opposite side mid points joining line segment is parallel to one of the parallel side.?
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Prove that opposite side mid points joining line segment is parallel to one of the parallel side.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Prove that opposite side mid points joining line segment is parallel to one of the parallel side.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove that opposite side mid points joining line segment is parallel to one of the parallel side.?.
Prove that opposite side mid points joining line segment is parallel to one of the parallel side.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Prove that opposite side mid points joining line segment is parallel to one of the parallel side.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove that opposite side mid points joining line segment is parallel to one of the parallel side.?.
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