Question

abc and dbc are two isosceles triangle on the same base bc if angle a = 70° , angle d = 60° find angle abd​

Answer 1

Solution

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

Answer 2

Step-by-step explanation:

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