Question

prove that triangle ABC is an isosceles triangle if median CE is perpendicular to base AB​

Answer 1

Answer:

Let AD be the median 

of △ ABC 

∴  In △ ABD & △ADC

AB=AC[isosceles triangle]

BD=DC [median]

∠ABD=∠ACD [ angle of isosceles triangle]

∴△ABD=△ADCso∠ADB=∠ADB

so∠ADB+∠ADC=180∘ [liner angle]

so∠ADC=90∘[median is perpendicular]

Hence proved.