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