Question

12. In triangle∆PQR = ∆PRQ, if we extend QR on both sides then two exterior
angles are formed. Let's prove that the measurement of external angles are equal.
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Answer 1

Step-by-step explanation:

HEY MATE .......

Let us first construct diagram for the above proof:

QR is extended on both the sides.

In the figure, ∠PQS and ∠PRT are the two exterior angles.

It is given that ∠PQR = ∠PRQ which means that the given triangle is an isosceles triangle.

Hence length PQ = PR.

Now ∠PQS + ∠PQR = 180° ……(i)

[as they form linear pair that angles in straight line always add up to 180°]

Similarly, ∠PRQ + ∠PRT = 180° ……. (ii).

For the equations (i) and (ii), the right-hand side is equal which means that the left-hand side should also be equal.

∠PQS + ∠PQR = ∠PRQ + ∠PRT∠PQS and ∠PRQ gets eliminated as they both are equal angles.

So, we can state that ∠PQS = ∠PRT.

Hence it is proved that the measurement of external angles is equal.

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