Question

In triangle ABC, AD is the perpendicular bisector of BC. show that triangleABC is an isosceles triangle in which AB=AC.​

Answer 1

Step-by-step explanation:

1.) in the triangle ABC let AD be the perpendicular Bisector of line BC making an angle of 90 degree on the line BC.

2.) in triangle ABD and ACD

AD=AD (common line)

angle ADC = angle ADC (given 90 degree)

BD=DC (given Bisector)

hence by SAS similarity Triangle ABD= ADC

therefore: Side AB = side AC (CPST)

since the opposite two sides are equal therefore triangle ABC is an Isosceles triangle.

Hence proved!