Question

ABC and DBC are two isosceles triangles on the same base BC.Show that angle ABD=angle ACD​

Answer 1

Step-by-step explanation:

∠ABD = ∠ABC + ∠CBD

∠ACD = ∠ACB + DCB

Both the triangles are isosceles, so the angles forming at the base would be equal.

So if ∠ABC = ∠ACB and ∠DBC = ∠BCD, the sum of ∠ABC + ∠DBC would be equal to the sum of ∠ACD and ∠BCD.

Hence, proved.

Answer 2

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