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


Answers (1)

Consider \DeltaABD  and  \DeltaADC,

(i)  AD\ =\ AD                       (Common in both the triangles)

(ii)   \angle ADB\ =\ \angle ADC       (Right angle)

(iii)  BD\ =\ CD                      (Since AD is the bisector of BC)

Thus by SAS congruence axiom, we can state :

                                              \Delta ADB\ \cong \ \Delta ADC

Hence by c.p.c.t., we can say that :           \small AB=AC

Thus   \Delta ABC is an isosceles triangle with AB and AC as equal sides.