Question

In ∆ABC, AB = AC. Show that the altitude AD is median also.

Answer 1

In ∆ABD and ∆ADC,

AB = AC                     ...(Since is an isosceles triangle)

AD = AD                     ...(common side)

∠ADB = ∠ADC            ...(Since AD is the altitude so each is 90°)

⇒ ΔADB ≅ ΔADC           ...(RHS congruence criterion) 

BD = DC               ...(cpct)

⇒ AD is the median.