To prove that a line parallel to a side of the triangle, the line intersects two sides

should separate the sides into corresponding segments of proportional lengths.

So, to prove , you have to show that .

Now determine the unknown measures.

Find NP.

                              (Apply Segment addition postulate)

                                  (Substitute )

                                        (Subtract 9 from each side)

Find RQ.

                             (Apply Segment addition postulate)

                           (Substitute )

                                          (Subtract 4.5 from each side)

Now determine whether the corresponding segments of sides are proportional.

                     (Substitute and simplify)

                                  (Substitute and simplify)

Since , sides have proportional lengths. So, .

The lines are parallel, .