Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 6 - Polygons and Quadrilaterals - 6-2 Properties of Parallelograms - Practice and Problem-Solving Exercises - Page 364: 19


$TU = 9$

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 transversals line $\overline{PS}$ is cut off in equal segments by the four parallel lines. We can then deduce that lines $VW$ and $TU$ are also transversals that are cut off in congruent segments by the same four parallel lines. We now know that $\overline{XZ}$ and $\overline{ZU}$ are congruent to $\overline{TX}$, so they all have lengths of $3$. Since $\overline{TU}$ is made up of all three segments, we just add the three segments together to find the total length of $TU$: $TU = TX + XZ + ZU$ Let's plug in what we know: $TU = 3 + 3 + 3$ Add to solve: $TU = 9$
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