Q12 of 14 Page 77

If 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.

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.


More from this chapter

All 14 →
9

Four rays meet at a point in such a way that measurement of opposite angles are equal. Let’s prove that two straight lines are formed by those four rays.

 10

Let’s prove that internal and external bisectors of an angle are perpendicular to each other.

 11

If two straight lines intersect each other four angles are formed. Let’s prove that the sum of measurement of the four angles is four right angles.

 13

Two straight lines intersect each other at a point and thus four angles are formed. Let’s prove that the bisectors of these angles are two perpendicular straight lines.