In the following figure,ABCDis a parallelogram and line segments AE and FC bisect the angles A and C respectively. Show that AE is parallel to FC

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Solution

GIven that AE and CF are angular bisectors. Now Angle ECF is equal to Angle BFC as both of them are corresponding angles
Also Angle EAF is equal to ECF as Angle A is equal to Angle C in a parallelogram.
so Angle EAF is equal to Angle BFC
As corresponding angles are equal, the lines will be parallel
So, AE is parallel to CF

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In the adjacent figure, ABCD is a parallelogram and line segments AE and CF bisect the angles A and C respectively. Show that AE || CF.

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