Question

In the given figure, AB =AC and DB = DC. Find the ratio of ∠ABD and ∠ACD .

Answer 1

hello,
in ΔABC
AB=AC
∴∠ABC=∠ACB(angles opposite to equal sides of a triangle are equal)......1
in ΔDBC,
DB=DC,
∴∠DBC=∠DCB(angles opposite to equal sides of a triangle are equal)......2
subtract 2 from 1
∠ABC-∠DBC=∠ACB-∠DCB(equals subtracted from equals gives equal)
=∠ABD=∠ACD
divide both the sides by ∠ACD
⇒∠ABD/∠ACD=1
∴∠ABD:∠ACD=1:1
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