Prove that?

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1 Answer
Aug 22, 2017

drawndrawn

Let AD, the perpendicular drawn from A to the angle bisector BD of /_ABC be produced to intersect BC at E.

Now in DeltaABD and DeltaEBD we have

  • /_ABD=/_EBD " given"

  • /_ ADB=/_ EDB, since BD perpendicular to AE

  • Side BD is common

So the triangles are congruent following Rigt angle Side Angle rule.
Hence AD=DE. This means D is the mid point of AE. So if a line is drawn through D parallel to EC or BC it will biseect AC.