PROVE THAT the bisector of an angle of a scalene triangle cannot be perpendicular to the opposite side..
Can any one give the explanation or discussion about this problem since i was absent that time when this topic is being discuss. Please give me hint how to do this ? thanks
Let ABC be a scalene triangle and D be the foot of the bisector of angle A at BC. Suppose that BC is perpendicular to AD, then it follows that angle DAB and angle ADB are congruent to angle DAC and angle ADC, respectively. Since AD=AD by reflexive property, then triangle ABD is congruent to triangle ACD by ASA, and thus AC = AB by CPCTC. But by defn. of Scalene triangle, AC cannot be congruent to AB and therefore a contradiction follows and the supposition is false and the theorem is true!