Question

In the figure MX = NY

MX and NY are parallel.

i) Are the sides of ∠MPX equal to the sides of ∠NPY ?

ii) what is the special about the postion of P on MN
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Answer 1

1. Yes
2. Point of intersection

Explanation:

SEE the image for solution.

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Answer 2

i) yes

ii) it splits MN in half (bisector)

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).