Geometry: Common Core (15th Edition)

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

Chapter 7 - Similarity - 7-5 Proportions in Triangles - Practice and Problem-Solving Exercises - Page 477: 40

Answer

Yes, the two red segments are parallel to one another. According to the side-splitter theorem, if a line is parallel to a side of a triangle and intersects the other two sides, then those two sides are divided proportionately. Let's set up a proportion for the sides whose values are given in the figure. If the ratios are equal to one another, then we can conclude that the red segments are parallel: $\frac{20}{16} = \frac{15}{12}$ Simplify each ratio by dividing the numerator and denominator by their greatest common factor: $\frac{5}{4} = \frac{5}{4}$ The ratios are equal to one another; therefore, the red segments are parallel to one another.

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