# Given :In Δ ABC: BD is perpendicular to AC, CE is perpendicular to AB and BD=CE.Prove:ΔABC is isosceles. refer to the pic

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by govindaBawa

Where is the pic????

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by govindaBawa

Where is the pic????

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<E=<D

BD=EC (given)

BC=BC (common)

hence,triangle (BEC=CDB) by RHS congruence criteria

i.e.<B=<C

so, AC=AB, (sides opposite to equal angles are equal)

thus,it is proved that ABC is an isosceles triangle