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: 39


No, the two red segments are not 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: $\frac{24}{10} = \frac{28}{12}$ Simplify each ratio by dividing the numerator and denominator by their greatest common factor: $\frac{12}{5} = \frac{7}{3}$ The ratios are not equal to one another; therefore, the red segments are not parallel to one another.

Work Step by Step

Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.