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If two parallel lines are intersected by a transversal, prove that the bisectors of the interior angles on the same side of transversal intersect each other at right angles.

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Given `AB||CD` and t is a transversal, cutting them at E and F respectively. Also, EG and FG, the bisectors of `angleBEFandangleDEF` respectively, meet at G. TO PROVE `angleEGF=90^(@)`
PROOF `AB||CD` and t is a transversal.
`:.angleBEF+angleDFE=180^(@)`
`[:'"co.int. "angle s" are " "supplementary"]`
`implies(1)/(2)angleBEF+(1)/(2)angleDFE=90^(@)impliesangle1+angle2=90^(@)." "....(i)`
But in `DeltaEGF` we have
`angle1+angle2+angleEGF=180^(@)" "["sum of the angles of a " Delta]`
`implies90^(@)+angleEGF=180^(@)" "["using (i)"]`
`impliesangleEGF=90^(@)`.
Hence, `angleEGF=90^(@)`.
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