CBSE Class 10 Sample Paper for 2024 Boards - Maths Standard

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Question 33 (a) - CBSE Class 10 Sample Paper for 2024 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at April 16, 2024 by

(a) State and prove Basic Proportionality theorem.

(b)  In the given figure ∠CEF = ∠CFE. F is the midpoint of DC. Prove that  AB/BD = AE/FD

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Transcript

Given: Ξ” ABC where DE βˆ₯ BC To Prove: 𝐴𝐷/𝐷𝐡 = 𝐴𝐸/𝐸𝐢 Construction: Join BE and CD Draw DM βŠ₯ AC and EN βŠ₯ AB. Proof: ar (ADE) = 1/2 Γ— Base Γ— Height = 1/2 Γ— AD Γ— EN ar (BDE) = 1/2 Γ— Base Γ— Height = 1/2 Γ— DB Γ— EN Divide (1) and (2) "ar (ADE)" /"ar (BDE)" = (1/2 " Γ— AD Γ— EN" )/(1/2 " Γ— DB Γ— EN " ) "ar (ADE)" /"ar (BDE)" = "AD" /"DB" Now, βˆ†BDE and βˆ†DEC are on the same base DE and between the same parallel lines BC and DE. ∴ ar (BDE) = ar (DEC) Hence, "ar (ADE)" /"ar (BDE)" = "ar (ADE)" /"ar (DEC)" "AD" /"DB" = "AE" /"EC" Hence Proved Now, let’s look at our question

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.