Answer:
i) yes
ii) it splits MN in half (bisector)
Step-by-step explanation:
We are given that MX and NY are parallel. This means, due to alternate interior angles, <XMN and <YNM are congruent as well as <MXY and <NYX. We are also given MX = NY. This is enough information to prove ΔMPX is congruent to ΔNPY due to ASA(two angles and a side between them).
(i) Now, because of this, we can say that all the sides of ΔMPX are congruent to those of ΔNPY. And, this means MP = NP. Since the point P divides the segment MN into two equal pieces, it's a bisector of MN(splits it in half).
