In the figure, $AB = AC$ and $DB = DC$, find the ratio $\angle ABD : \angle ACD$.
"
Given:
In the given figure, $AB = AC$ and $DB = DC$.
To do:
We have to find the ratio $\angle ABD : \angle ACD$.
Solution:
In $\triangle ABC$,
$AB = AC$
$\angle ACD = \angle ABE$..........…(i) (Angles opposite to equal sides are equal)
In $\triangle DBC$,
$DB = DC$
This implies,
$\angle DCB = \angle DBC$...........(ii)
Subtracting (ii) from (i), we get,
$\angle ACB - \angle DCB = \angle ABC - \angle DBC$
$\angle ACD = \angle ABD$
Therefore,
Ratio of $\angle ABD : \angle ACD = 1 : 1$.
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