Exercise 4 Page 577

We are given a triangle △JKL and we want to determine whether the segments JL and MP are parallel.

By the Converse Triangle Proportionality Theorem, if a line intersects two sides of a triangle and separates the sides into proportional corresponding segments, then the line is parallel to the third side of the triangle. Let's check if the sides are divided proportionally. JM/MK ? = LP/PKSince we are given the lengths of JM and JK, we can find the length of MK.

Similarly we are given the lengths of PK and LK, so we can find the length of LP.

Now we can substitute all known lengths into our proportion. JM/MK ? = LP/PK ⇕ 5/10 ? = 4/9 We will simplify each ratio as much as possible to see if they are equivalent.

As we can see, the sides are not divided proportionally. Therefore, segments JL and MP are not parallel.