ABCD is a rhombus, EABF is a straight line such that EA = AB = BF. Prove that ED and FC when produced meet at right angles.
Rhombus ABCD is given:
We have
We need to prove that 
We know that the diagonals of a rhombus bisect each other at right angle.
Therefore,
,
,
In 
A and O are the mid-points of BE and BD respectively.
By using mid-point theorem, we get:
Therefore,
In 
A and O are the mid-points of BE and BD respectively.
By using mid-point theorem, we get:
Therefore,
Thus, in quadrilateral DOCG,we have:
and
Therefore, DOCG is a parallelogram.
Thus, opposite angles of a parallelogram should be equal.
Also, it is given that
Therefore,
Or,
Hence proved.