Question

In tiangle ABC,AD is the perpendicular bisector of BC.show that triangle ABC is an isosceles triangle in which AB = AC.

Answer 1

T HE ANSWER TO THE GIVEN QUESTION IS ATTACHED WITH THIS 

Answer 2

AD $\perp$ BC (given)

TO BE SHOWN :
ΔABC is an isosceles triangle

SOLUTION :

ΔBDA and ΔDAC

BD = DC [ $\therefore$ AD $\perp$ BC ]

$\angle{ADB}$ = $\angle{ADC}$ = 90° each

AD = AD (common side)

Hence, by $\bf{SAS}$ congruence condition ΔADB $\cong$ ΔADC

Now,

$\angle{B}$ = $\angle{C}$ [ by CPCT ]

$\therefore$ AB = AC

Hence proved.