Question

ABC is a triangle with B as midpoint of Ab D is perpendicular to AC and DF is perpendicular to BC also be a is equal to DF prove prove that triangle ABC is an isosceles triangle

Answer 1

Hello Mate Here Is Your Answer
Let the perpendicular from D to AB meet at O and AC meet at P

Then in ∆ AOD and ∆ APD

angle P= angle O= 90°

Given DO=DP

AD common

So ∆AOD=∆APD (As per RHS )

As per CPCT

AO=AP eq-1

Same we can prove ∆DOB=∆DOC

And OB=OC eq-2

Adding the eq-1 and eq-2 we get

AO+OB=AO+OC

=>AB=AC

Hope you get it.

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