Exercise 16 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/YX We have to find and simplify each ratio. We will start from the left-hand side of the proportion.

To find the right-hand side, let YX=x. Since we are told that YX= 12WY, WY=2x.

Now we can compare both sides of our proportion. ZV/VX ? = WY/YX ⇕ 4 ≠ 2 As we can see, the sides are not divided proportionally. Therefore, segments VY and ZW are not parallel.