Question

ABCD is a kite in which BC = CD, AB = AD. E, F and G are the mid-points of CD, BC and AB respectively. Prove that: The line drawn through G and parallel to FE and bisects DA.

Answer 1

In ΔABD,
G is the mid-point of AB and HG || BD    ...(from (ii) EF || DB and EF || HG)
Therefore, HG || DB
Therefore, H is the mid-point of DA.
Hence, the line drawn through G and parallel to FE bisects DA.