Question

In ABC, AD is the perpendicular bisector of BC. Show that ABC is

an isosceles triangle in which AB = AC

A



B C​

Answer 1

Step-by-step explanation:

$\tt\large\underline\purple{Answer}$

In △ABD and △ACD, we have 

DB=DC ∣ Given

∠ADB=∠ADC ∣ since AD⊥BC

AD=AD ∣ Common

∴ by SAS criterion of congruence, we have.

△ABD≅△ACD

⇒AB=AC ∣ Since corresponding parts of congruent triangles are equal

Hence, △ ABC is isosceles.