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Question
Solve the following question using appropriate Euclid’s axiom:
In the following figure, we have ∠ABC = ∠ACB, ∠3 = ∠4. Show that ∠1 = ∠2.
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Solution
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 equation (ii) from equation (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.
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