## Geometry: Common Core (15th Edition)

Published by Prentice Hall

# Chapter 6 - Polygons and Quadrilaterals - Mid-Chapter Quiz - Page 398: 14

#### Answer

$AE = 20.6$

#### Work Step by Step

Theorem 6-7 states that if three or more parallel lines cut off congruent segments off of a transversal, then they will cut off congruent segments off of any transversal. We see from the diagram that the transversal $\overline{BF}$ is cut off in equal segments by the three parallel lines. We can then deduce that line $AE$ is also a transversal that is cut off in congruent segments by the same three parallel lines. We now know that $AC$ is congruent to $CE$, so they both have a length of $10.3$. We are asked to find the length of $\overline{AE}$. We can do this by adding the lengths of the two segments $\overline{AC}$ and $\overline{CE}$ together: $AE = AC + CE$ Let's plug in what we know: $AE = 10.3 + 10.3$ Add to solve for $AE$: $AE = 20.6$

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