Given: in triangle ABC,AB=AC
Draw perpendicular from point A on line BC which cut at point D
Consider, triangles ADB and ADC
AB=AC (Given)
∠ADB=∠ADC=90o .... [Since AD perpendicular on BC]
AD=AD [Common side]
∴△ADB≅△ADC ..... [By SAS congruence rule]
∴∠B=∠C
∴ In △ABC,∠B=∠C
Thus, △ABC is an isosceles triangle.
Hence, option C is correct.