(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




Given: Δ ABC where DE ∥ BC To Prove: 𝐴𝐷/𝐷𝐵 = 𝐴𝐸/𝐸𝐶 Construction: Join BE and CD Draw DM ⊥ AC and EN ⊥ AB. Proof: ar (ADE) = 1/2 × Base × Height = 1/2 × AD × EN ar (BDE) = 1/2 × Base × Height = 1/2 × DB × EN Divide (1) and (2) "ar (ADE)" /"ar (BDE)" = (1/2 " × AD × EN" )/(1/2 " × DB × EN " ) "ar (ADE)" /"ar (BDE)" = "AD" /"DB" Now, ∆BDE and ∆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

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.