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

Consider $\Delta$ABD  and  $\Delta$ADC,

(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.

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