Exercise 35 Page 599

We are given a triangle △ABE and we want to determine whether the segments AB and CD are parallel.

Let's make a proof by contradiction. To do so, we have to assume that the segments AB and CD are parallel. Therefore, according to the Corresponding Angles Theorem and Angle-Angle Similarity Theorem, △ ABE and △ CDE are similar.

Since △ ABE ~ △ CDE, their corresponding sides must be proportional. Let's check it. AB/CD ? = AE/CE ⇔ 8/4 ? = 9/4 We will simplify each ratio as much as possible to see if they are equivalent.

As we can see, the sides are not proportional. Therefore, the assumption was false, so segments AB and CD are not parallel.