Q. 84.2( 10 Votes )

On side AB of ΔABC two points D and E lie such that AD = BE. If DP || BC and EQ || AC then prove that PQ || AB.

Answer :


In ΔABC,


EQ||AC


By Basic Proportionality Theorem,



AD = BE |Given


AE = AD + DE = BE + ED = BD


…(1)


In ΔABC,


DP||BC


By Basic Proportionality Theorem,


…(2)


From (1) & (2),



By Converse of BPT, PQ||AB.


Hence, proved.


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Rajasthan Board Mathematics