(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
CBSE Class 10 Sample Paper for 2024 Boards - Maths Standard
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CBSE Class 10 Sample Paper for 2024 Boards - Maths Standard
Last updated at April 16, 2024 by Teachoo
Given: Ξ ABC where DE β₯ BC To Prove: π΄π·/π·π΅ = π΄πΈ/πΈπΆ Construction: Join BE and CD Draw DM β₯ AC and EN β₯ 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, βBDE and βDEC are on the same base DE and between the same parallel lines BC and DE. β΄ ar (BDE) = ar (DEC) Hence, "ar (ADE)" /"ar (BDE)" = "ar (ADE)" /"ar (DEC)" "AD" /"DB" = "AE" /"EC" Hence Proved Now, letβs look at our question