Let ABC be triangle and D and E be two pobcints on side AB such that AD=BE. if DP||BC and EQ||AC, then prove PQ||AB
given: ABC is a triangle. AD = BE.
DP || BC and EQ || AC
TPT: PQ || AB
in the triangles ADP and EBQ;
AD = BE (given)
∠DAP = ∠BEQ [corresponding interior angles]
∠ADP = ∠EBQ [corresponding interior angles]
therefore by ASA congruency triangle ΔADP ≡ ΔEBQ
thus by CPCT : PD = BQ..........(1)
and PD || BQ [given]......(2)
since one pair of opposite side are equal and parallel.
therefore quadrilateral DPQB is a parallelogram and
PQ || DB
i.e. PQ || AB
which is the required result.
hope this helps you.