Exercise 14 Page 578

We are given a triangle △ZWX and we want to determine whether segments VY and ZW 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. ZV/VX ? = WY/YXSince we are given the lengths of ZV and ZX, we can find the length of VX.

Similarly, we have the lengths of YX and WX. Let's find the length of WY.

Now we can substitute all known lengths into our proportion. ZV/VX ? = WY/YX ⇕ 6/12 ? = 8/16 We will simplify each ratio as much as possible to see if they are equivalent.

As we can see, the sides are divided proportionally. Therefore, segments VY and ZW are parallel.