If ab is extended to e of a parallelogram abcd in such that ab= be,and de cuts bc at q then find qc:qb
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Answer: AB = DC (Opposite sides of a parallelogram are equal)
AB = BE (Given)
Therefore, BE = DC
IN TRIANGLES QEB AND QCD: Angle DQC = Angle EQB (vertically opposite angles are equal)
Angle BEQ = Angle CDQ (Alternating interior angles are equal)
BE = DC (Proved)
Therefore Triangle QEB is Congruent to Triangle QCD by AAS criterion.
Therefore, QC = QB
Therefore, QC:QB = 1
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