Question

In Fig. 10.25, 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, Δ ABC  and Δ DBC are isosceles triangles since AB= AC  and DB = DC respectively  

⇒∠ABC = ∠ACBand ∠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