Question

in the figure,AD=BD,DE||BC and FD||CE.prove that DE=BF

Answer 1

Here ,
BF=FC (F is the mid point). (1)
given that ,
FC=DE. (opposite sides are parallel of llgm) (2)
from eq 1 and 2, we get,
BF =DE

Answer 2

In triangle ADE and DBF
AD = BD
angle ADE = angle ABF (coz DE || BC)
angle AED = angle DFB (coz DE || BC and FD || CE)

then by AAS criteria triangle ADE is congruent to DBF
then by cpct DE = BF.

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