Premium Online Home Tutors
3 Tutor System
Starting just at 265/hour

# In the $$\triangle{ABC}$$, AD is the perpendicular bisector of BC (see figure). Show that $$\triangle{ABC}$$ is an isosceles triangle in which AB = AC.

In $$\triangle{ABC}$$ and $$\triangle{ACD}$$, we have,

DB = DC ...(given)
$$\angle{ADB}$$ = $$\angle{ADC}$$ ...(Since, AD is the perpendicular bisector of BC)

and AD is the Common side.

Therefore, $$\triangle{ABD}$$ $$\displaystyle \cong$$ $$\triangle{ACD}$$ ...(By SAS congruency test)

Therefore, AB = AC ...(By CPCT)

Hence, $$\triangle{ABC}$$ is an isosceles triangle.
Hence, proved.