Question

triangle abc and triangle dbc are two isosceles triangles on the same base bc .show that angle abd=angle acd

Answer 1

Answer:

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

hence,angle abd= angle acd proved