Question

In the given figure, `AB||CD` and a transversal t cuts them at E and F respectively. If EP and FQ are the bisectors of `angleAEF` and `angleEFD` respectively, prove that `EP||FQ`.

Answer 1

`AB||CD` and t is the transversal.
`:. angleAEF=angleEFD` [alt. int. `angles`]
`implies 1/2 angleAEF=1/2 angleEFD`
`implies angleFEP=angleEFQ`
But these are alternate interior angles.
Hence, `EP||FQ`.