Question

In the given figure if PQ||RS prove that ​

Answer 1

From the triangles POQ & ROS above,

<POQ=<ROS (vertically opposite angles)

<QPO=<RSO (alternate angles)

<QPO = <SRO(alternate angles)

Therefore, triangle POQ=triangle ROS (PROVED by AAA similarity)

Therefore by cpct(common parts of congruent triangles) PQ ||RS

Answer 2

Explanation:

Since PQ || RS, hence PS is a traversal:

=> angle QPS = angle RSP ---(a)

Now similarly, QR is a traversal:

=> angle PQR = angle SRQ ---(b)

Now, we can clearly see that,

angle POQ = angle SOR (vertically opposite angles) --(c)

Hence from (a), (b) and (c), We can say:

∆POQ ~ ∆SOR (AAA similarity)

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