2. In .d ABC, AD is the perpendicular ffi => L OAB = L OAC => AO bisects L BAC. A [CPCT] bisector of BC (see figure ). Show that .d ABC is an isosceles triangle in which AB = AC.

Since AD is perpendicular bisector of BC. . . BD = CD and LADB = LADC = 90° ...(i) Consider triangles ADB and ADC, We have BD = DC and LADB = LADC AD = AD A ADB ::: A ADC AB = AC. [From (i)] [Common] [SAS rule] Therefore, .1ABC is an isosceles triangle with AB = AC. [CPCT]