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Introduction to Euclid's Geometry
Question
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In the given figure, it is given that ∠1 = ∠4 and ∠3 = ∠2. By which Euclid's axiom, it can be shown that if ∠2 = ∠4, then ∠1 = ∠3.

Answer

∠2 = ∠4     ...(1) | Given
∠1 = ∠4     ...(2) | Given
∠3 = ∠2     ...(3) | Given
From (1),
∠4 = ∠2    ...(4)
From (3) and (4),
∠3 = ∠4    ...(5)
| Things which are equal to the same thing are equal to one another
From (2) and (4),
∠1 = ∠3
|Things which are equal to the same thing are equal to one another

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