In Fig. 10.25, AB = AC and DB = DC , find the ratio ∠ ABD : ∠ ACD .

Question

In Fig. 10.25, AB = AC and DB = DC , find the ratio &#x2220; ABD : &#x2220; ACD .

Philoid · Accepted Answer

Consider the figure,

Given,

AB = AC

DB = DC

To find: Ratio ∠ABD =∠ACD

Now, 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