Question

prove that perpendicular AD drawn to the base BC of an isosceles triangle ABC from the vertex A bisects BC that is BD is equals to DC

Answer 1

U can use RHS congruence rule.
In ∆ADB and ∆ADC
angleADB=angleADC=90° (since AD is perpendicular to BC)

AB=AC( since it is an isos triangle)
AND. AD=AD (common)
therefore the triangles are congruent.
BD=DC(by cpct)

hope it helps u.