Question
Mathematics Question on Intersecting Lines and Non-intersecting Lines
In Figure, ∠PQR = ∠PRQ, then prove that ∠PQS = ∠PRT.
Answer
In the given figure, ST is a straight line and ray QP stands on it.
∴ ∠PQS + ∠PQR = 180º (Linear Pair)
∠PQR = 180º − ∠PQS............ (1)
∠PRT + ∠PRQ = 180º (Linear Pair)
∠PRQ = 180º − ∠PRT............ (2)
It is given that ∠PQR =∠ PRQ.
Equating equations (1) and (2), we obtain
180º − ∠PQS = 180º− ∠PRT
∠PQS = ∠PRT