Q. 114.2( 5 Votes )

# In Fig. 10.25, *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, 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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