△ABC and △DBC are two isosceles triangles on the same base BC (see figure). Show that ∠ABD=∠ACD
Given ΔABC and ΔDBC are two isosceles triangles on the same base BC
In isosceles ΔABC
AB=AC
Then ∠ABC=∠ACB................................(1)
In isosceles ΔBDC
BD=DC
Then ∠CBD=∠BCD..................................(2)
Add (1) and (2) we get
∠ABC+∠CBD=∠ACB+∠BCD
But ΔABC and ΔDBC on same base
∴∠ABD=∠ACD