Mathematics
In the figure, AB = AC and DB = DC. ∠ABD : ∠ACD is :
1 : 2
2 : 1
1 : 1
1 : 3
Triangles
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Answer
In △ABC,
AB = AC
⇒ ∠B = ∠C = x ….(1) (let) (Angles opposite to equal sides in a triangle are equal)
In △BDC,
BD = CD
⇒ ∠DBC = ∠DCB = y ….(2) (let) (Angles opposite to equal sides in a triangle are equal)
Subtracting eq.(2) from (1), we have :
⇒ ∠B - ∠DBC = ∠C - ∠DCB
⇒ ∠ABD = ∠ACD
⇒ ∠ABD : ∠ACD = 1 : 1.
Hence, option 3 is the correct option.
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