MP is parallel to IJ
What is triangle Parallel Side Theorem?
When a line is drawn parallel to one side of a triangle, it creates a smaller triangle with sides parallel to the corresponding sides of the original triangle.
From the figure
MN is drawn parallel to HJ
MN is a transversal that intersect HI and JI at M and N respectively.
Points M and N are extended to meet line HJ at P, creating smaller triangles MNP and HPM
Due to the parallelism, MNPH is a parallelogram with MP as diagonal, the corresponding sides of these smaller triangles are parallel. MP and JI are parallel (by construction).MN and HP are parallel (definition of parallelogram)
Therefore,MP is parallel to IJ.