Question

In the given figure, `AB||CD` and a transversal t cuts them at E and F respectively. If EG and FG are this bisectors of `angleBEF` and `angleEFD` respectivelym prove that `angleEGF=90^(@)`.

Answer 1

`angleBEF+angleDFE=180^(@)`
`implies 1/2 angleBEF+1/2 angleDFE=90^(@)`
`implies angleGEF+angleGFE=90^(@)`. ltbr. In `DeltaEGF`, we have
`angleGEF+angleGFE+angleEGF=180^(@) implies angleEGF=90^(@)`.