`A B C D` is a rhombus, `E A B F` is a straight line such that `E A=A B=B F` . Prove that `E D` and `F C` when produced meet at right angles.

Explanation

To prove:`/_ DGC=90^0`

Proof: diagonals of a rhombus bisect each other at right angles

`therefore OA=OC=,OB=OD`

`/_AOD=/_COD=/_AOB=/_BOC=90^0`

`In /_\BDE, O and A` are midpoints of BD and BC `

`therefore AO"//"ED`

"similarly, "OC "//"DG`

`In /_\CFA, D and "B are midpoints of "AC and AF`

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