Question:
In Fig. (10).2(5) AB = AC and DB = DC, find the ratio ∠ABD: ∠ACD.
Solution:
Consider the figure
Given,
AB = AC, DB = DC and given to find the ratio
∠ABD = ∠ACD
Now, ΔABC and ΔDBC 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
