Question

In a AABC, AB = AC. If D is the mid-point of
the side BC, prove that:
(i) AD IBC (ii) AD bisects BAC.

Answer 1

Answer:

In △ABD and △ACD,

∠BAD=∠CAD (Given)

AD=AD (Common)

AB=AC (Given)

Thus, △ABD≅△ACD (SAS rule)

Hence, BD=CD (By cpct)

∠ADB=∠ADC=x (By cpct)

∠ADB+∠ADC=180

x+x=180

x=90

∘

Thus, ∠ADB=∠ADC=90

∘

Hence, AD is perpendicular bisector of BC