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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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Answer» given , BD = CE To prove - ΔBEC is congruent to ΔBDC proof , BD = CE ( Given ) angle BEC = angle BDC ( Given ) BC = BC ( common ) by SAS ΔBEC is congruent to ΔBDC , therefore , angle EBC = DCB ( C.P.C.T ) therefore, ΔBEC is isosceles ( because by the property of isosceles triangle base ANGLES are equal ) |
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