2. In ΔABC, AD is the perpendicular bisector of BC (see Fig. 7.30). Show that ΔABC is an isosceles triangle in which AB = AC.
Solution: It is given that AD is the perpendicular bisector of BC To prove: AB = AC Proof: In ΔADB and ΔADC, AD = AD (It is the Common arm) ∠ADB = ∠ADC BD = CD (Since AD is the perpendicular bisector) So, ΔADB ≅ ΔADC by SAS congruency criterion. Thus, AB = AC (by CPCT)
