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In Fig. 6.40, E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD perpendicular BC and EF perpendicular AC, prove that triangle ABD similar triangle ECF.

Q11  In Fig. 6.40, E is a point on side CB produced of an isosceles triangle ABC
        with AB = AC. If AD \perp BC and EF \perp AC, prove that \Delta ABD \sim \Delta ECF
  

        

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To prove : \Delta ABD \sim \Delta ECF

Given: ABC is an isosceles triangle.

AB=AC \, \, and\, \, \angle B=\angle C

In \Delta ABD \, \, and\, \, \Delta ECF,

     \angle ABD=\angle ECF         (\angle ABD=\angle B=\angle C=\angle ECF)

    \angle ADB=\angle EFC        ( Each 90 \degree)

\Delta ABD \sim \Delta ECF          ( By AA criterion)

 

 

 

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