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  • Solve each of the following question using appropriate Euclid’s axiom: In the Fig. 5.9, we have angle ABC equal to angle ACB, angle 3 equal to angle 4. Show that angle 1 equal to angle 2.

Solve each of the following questions using appropriate Euclid’s axiom:  In Fig. 5.9, we have \angleABC = \angleACB, \angle3 = \angle4. Show that \angle1 = \angle2.

Answers (1)

Given that: \angleABC = \angleACB, \angle3 =\angle4

To prove: \angle1 = \angle2

Euclid’s axiom says that if equals are subtracted from equals, then remainders are also equal.

So, as \angleABC = \angleACB, \angle3=\angle4

We can write,

\angleABC - \angle4 =\angleACB –\angle3

Now, (\because \angleABC = \angle1 + \angle4 ;\angleACB = \angle2 + \angle3)

\angle1 = \angle2

Hence proved

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