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InterviewSolution
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What is BPT Theorm |
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Answer» Theorem: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.Ans.Given:ABC is a∆BC||DETo Prove:AD by BD=AE by ECConstruction:Join DC and BE Draw ENperpendicular to AB and DM perpendicular to AE.Proof:BC||DE(given)ar.∆BDE = ar.∆DEC....................eq.1(∆on same base bet.same parallel.)ar.ADE by ar.BDE=1/2×AD×EN by 1/2×BD×ENar.ADE by ar.BDE=AD by BD.............eq.2ar.AED by ar.DEC=1/2×AE×DM by 1/2×EC×DMar.AED by ar.DEC=AE by EC..............eq.3Comparing 2 and 3 using 1ar.ADE by ar.BDE=ar.AED by ar.DECAD by BD=AE by EC(proved){AD by BD+1=AE by EC+1AD+BD by BD= AE+EC by ECAB by BD=AC by ECTaking reciprocalBD by AB= EC by AC1-BD by AB= 1-EC by ACAB-BD by AB= AC-EC by ACAD by AB =AE by AC}corrolary. According to this theorm ,a line is drawn parallel to the one side of a triangle to interset the other two sides in distinct points then the other two sides are divided in same ratio. If in triangle ABC , DE parallel AD then by BPT theorm AD/DB equal AE/EC |
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