Theorem 6.1 Basic proportionality theorem (BPT) : If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio Class 10 December 30, 2022December 27, 2022 by admin Given : △ABC in which a line parallel to side BC intersects other two sides AB and AC at D and E respectively.To prove : AD/DB = AE/ECConstruction : Join BE and CD and draw DM and EN perpendicular to AC and AB respectively.Proof : area of △ADE = ½ × base × height So, ar(ADE) = ½ × AD × ENSimilarly, ar(BDE) = ½ × BD × ENar(ADE) = ½ × AE × DM and ar(DEC) = ½ × EC × DMNote that △BDE and △DEC are on the same base DE and between the same parallels BC and DE.So, ar(BDE) = ar(DEC)…….(iii)Therefore, from (i), (ii) and (iii), we have :Share this:FacebookMoreEmailWhatsAppLike this:Like Loading...Related