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

1.	In Fig., AB = AC and DB = DC, find the ratio ∠ABD :∠ACD.
Answer» Consider the figure, Given, AB = AC DB = DC To find: Ratio ∠ABD =∠ACD Now, ΔABC and ΔDBC 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

Answer»

Consider the figure,

Given,

AB = AC

DB = DC

To find: Ratio

∠ABD =∠ACD

Now, ΔABC and ΔDBC 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

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