In the given figure, `AB||CD` and a transversal t cuts them at E and F – InterviewSolution

1.	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» `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`.

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