Question

In the following figure assume NR=PS and MR=QS, and angle OSR is congruent to angle ORS. Prove that angle M is congruent to angle Q. Write in statement and reason form.

Answer 1

All you have to do is state that Point O is on segments PS and NR. Then you can say that OSR is congruent to PSR
NRM is conguent to ORM

and prove by SAS

Answer 2

Or you can that segments NR and PS intersect @ Point O, then proceed from there.

Answer 3

If two segments intersect at a point, then that point must exist on both segments