Question

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.

Answer 1

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.