Question

In figure AD is the bisector of ∠A such that AD | BC. Is ∆ABC an isosceles triangle?
Give reasons on support of your answer.

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.