Exercise 3 Page 577

We are given a triangle △ABC and we want to determine whether the segments DE and AB 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. AD/DC ? = BE/EC Since we are given lengths of BE and BC, we can find length of EC.

Now we can substitute all known lengths to our proportion. AD/DC ? = BE/EC ⇕ 8/12 ? = 6/9 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 DE and AB are parallel.