Question

In ∆ ABC, AD is the perpendicular bisector of BC (see Fig. 7.30). Show that ∆ ABC is an isosceles triangle in which AB = AC.

Answer 1

In ∆ADC and ∆ADB, 

AD = AD (Common) 

∠ADC = ∠ADB (Each 90º)

CD = BD (AD is the perpendicular bisector of BC)

∠∆ADC ∠∆ADB (By SAS congruence rule)

∴ AB = AC (By CPCT)