Prove that?

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1 Answer
Aug 22, 2017

drawn

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.