Question

in triangle ABC,AD is the perpendicular bisector of BC show that triangke ABC is an isosceles triangle in which AB=AC

Answer 1

we know that angles opposite to equal sides are also equal
so angle ABC = angle ACB
proved that it is a isosceles triangle
hope it will help you

Answer 2

IN TRIANGLE ABD and ACD,
AD=AD. (common)
angle ADB=angle ADC. (90°)
BD=CD. (since BD is bisector of BC)
so triangle ABD~=ACD

so AC=AB. (CPCT)