Question

In figure, AB = AC and DB = DC, find the ratio ∠ABD : ∠ACD 

 

Answer 1

Consider the figure Given

AB = AC, DB = DC and given to find the ratio

∠ABD = ∠ACD

Now,∠ABC and ∠DBC are isosceles triangles since AB = AC and

DB = DC respectively

⇒ ∠ABC = ∠ACB and ∠DBC = ∠DCB       [ ∵ angles opposite to equal sides are equal]

Now consider,

∠ABD : ∠ACD

⇒ (∠ABC - ∠DBC ) : (∠ACB - ∠DCB)

⇒ (∠ABC - ∠DBC ) : (∠ABC - ∠DBC )       [∵∠ABC - ∠ACB and ∠DBC = ∠DCB]

⇒  1:1

∴∠ABD :∠ACD = 1:1