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In the adjoining figure, we have ∠ABC = ∠ACB and ∠3 = ∠4. Show that BD = DC.
Given, ∠ABC = ∠ACB …(i)
and ∠4 = ∠3 …(ii)
According to Eulid’s axiom, if equals are subtracted from equals, then remainders are also equal.
On subtracting Eq. (ii) from Eq. (i), we get
∠ABC – ∠4 = ∠ACB – ∠3 =>∠1 = ∠2
Now, in ABDC, ∠1=∠2
=> DC =BD [sides opposite to equal angles are equal]
BD = DC.