CBSE Class 10 Sample Paper for 2025 Boards - Maths Standard
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CBSE Class 10 Sample Paper for 2025 Boards - Maths Standard
Last updated at Sept. 26, 2024 by Teachoo
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Question 26 (B) In π₯ABC, P and Q are points on AB and AC respectively such that PQ is parallel to BC. Prove that the median AD drawn from A on BC bisects PQ. We need to prove R is mid-point of PQ i.e. PR = RQ Since PQ β₯ BC And AB is transversal β APR = β ABD Similarly, PQ β₯ BC And AC is transversal β AQR = β ACD In Ξ APR & Ξ ABD β PAR = β BAD β APR = β ABD Ξ APR ~ Ξ ABD Since ratio of sides of similar triangle are equal π¨π·/π¨π©=π·πΉ/π©π« In Ξ AQR & Ξ ACD β QAR = β CAD β AQR = β ACD Ξ AQR ~ Ξ ACD Since ratio of sides of similar triangle are equal π¨πΈ/π¨πͺ=πΈπΉ/πͺπ« Also, In Ξ APQ & Ξ ABC β APQ = β ABC β AQP = β ACB Ξ APQ ~ Ξ ABC Since ratio of sides of similar triangle are equal π¨π·/π¨π©=π¨πΈ/π¨πͺ And from (1) and (2) π¨π·/π¨π©=π·πΉ/π©π« & π¨πΈ/π¨πͺ=πΈπΉ/πͺπ« From (1), (2) and (3) π·πΉ/π©π«=πΈπΉ/πͺπ« Since BD = CD given ππ /π΅π·=ππ /π΅π· PR = QR Hence proved
