Question

Solve the following question using appropriate Euclid’s axiom:

In the following figure, we have ∠ABC = ∠ACB, ∠3 = ∠4. Show that ∠1 = ∠2.

Answer 1

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.