Question

Please Help Me. I need to figure out if MN is parallel to PQ but I don't know how to solve it.

Answer 1

By checking proportion formula, we conclude that line segments MN and PQ are not parallel. (Right choice: D)

How to determine if line segments MN and PQ are parallel

Herein we have the case of a geometric system consisting in two triangles, in which we must check if line segments MN and PQ are parallel. It happens if and only if triangles MNR and PQR are similar, whose proportion formula should be:

`(QR)/(NR) = (PR)/(MR)`

If we know that QR = 48, NR = 84, PR = 54 and MR = 96, then the proportion formula is checked:

`(48)/(84) = (54)/(96)`

Thus, by simplification of fractions:

`(4)/(7) = (9)/(16)` (FALSE)

Line segments MN and PQ are not parallel.