Question

in fig.6.15∠PQR=∠PRQ,then prove that ∠PQS=PRT

Answer 1

PQR = PRQ equation 1

PQR+PQS = PRQ + PRT

from equation 1

we have

PQR + PQS= PQR +PRT

PQS = PRT (PQR is cancelled )

hence proved

Answer 2

Question :-

In figure, ∠PQR = ∠PRQ, then prove that ∠PQS = ∠PRT.

Answer :-

ST is a straight line.

∴ ∠PQR + ∠PQS = 180° …(1) [Linear pair]

Similarly, ∠PRT + ∠PRQ = 180° …(2) [Linear Pair]

From (1) and (2), we have

∠PQS + ∠PQR = ∠PRT + ∠PRQ

But ∠PQR = ∠PRQ [Given]

∴ ∠PQS = ∠PRT

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