Exercise 34 Page 599

We are given a triangle △ABE and we want to determine whether the segments AB and CD 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. AC/CE ? = BD/DEWe are given that AC=7 and AE=15. We can use this information to find the length of CE.

Similarly, we are given that BD=10.5 and BE=22.5. Let's find length of DE.

Now we can substitute all known lengths to our proportion. AC/CE ? = BD/DE ⇔ 7/8 ? = 10.5/12 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, the segments AB and CD are parallel.