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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