Question

In the following figure, PQ||RS and a transversal AB cuts them at O and L. if OM and LN are the angle bisector of ROL and OLQ respectively prove that OM || LN​

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

We have, PQ||RS and AB is transversal,

Therefore, angle ROL = angle OLQ ( alternate interior angles)

Multiplying by 1/2 on both sides,

1/2(angle ROL) = 1/2(angle OLQ)

We get, angle MOL = angle OLN ( OM and LN are angle bisectors of angle ROL and angle OLQ respectively)

Now, we have angle MOL = angle OLN ,

But these are alternate interior angles.

Therefore, by converse of alternate angle theorem,

We get , OM||LN.

Hence, proved.