Question

In ∆ ABC ,AB is the perpendicular bisects of BC . show that ∆ ABC is an isosceles triangle in which AB = AC

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Answer 1

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.