Question

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

Answer 1

Consider the figure,

Given,

AB = AC

DB = DC

To find: Ratio

∠ABD =∠ACD

Now, ΔABC and ΔDBC are isosceles triangles

Since,

AB = AC

And,

DB = DC

Therefore,

∠ABC = ∠ACB and,

∠DBC = ∠DCB (Angle opposite equal sides)

Now, consider ∠ABD : ∠ACD

(∠ABC - ∠DBC) : (∠ACB - ∠DCB)

(∠ABC - ∠DBC) : (∠ABC - ∠DBC) [Since, ∠ABC = ∠ACB and ∠DBC = ∠DCB]

1: 1

Therefore,

∠ABD : ∠ACD = 1:1