Exercise 2 Page 577

Let's analyze the given figure. Since we are given a triangle with a line that is parallel to one of its sides, we can use the Triangle Proportionality Theorem.

The lengths of the segments intercepted by the parallel line are proportional. Let's write a proportion using the expressions for the lengths of the segments. XN/NZ=XM/MY Since we are given the lengths of XM and XY, we can find the length of MY.

Now we can substitute all known lengths into our proportion. XN/NZ=XM/MY ⇕ 6/NZ=2/8 Finally, we will solve this equation for NZ.