Are the Segments Parallel? Yes. Explanantion: See solution.
Practice makes perfect
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 substitute in the lengths provided and see if the sides are divided proportionally.
AC/CE ? = BD/DE ⇔ 8.4/6 ? = 6.3/4.5
We will simplify each ratio as much as possible to see if they are equivalent.
