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.

8/4 ? = 9/4

CalcQuot

Calculate quotient

2 ≠ 2.25

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