exam

consider triangles ABD,ACD

AB=AC  (given triangle is equilateral)

angle ABD=angle ACD....(Each equal to 60 degrees given)

BD=CD..(Snce AD is median)

so

 triangle ABD congruent to triangle ACD(SAS rule)

so,

angleBAD =angle CAD (C.P.C.T.)

Also

angle ADB=angle ADC (C.P.C.T.)...(i)

But they form a linear pair

so

ADB+ADC=180

 So

2ADB=180...(from i)

So

ADB=90 degrees

AD perpen. to BC.