Geometry: Common Core (15th Edition)

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

Chapter 5 - Relationships Within Triangles - Chapter Test - Page 345: 15

Answer

$\overline{DE} \parallel \overline{BC}$, and $BC$ is two times as long as $DE$.

Work Step by Step

From the diagram, we have a line segment $\overline{DE}$ that joins the midpoint $D$ on one side of the triangle and joins midpoint $E$ on the other side of the triangle. According to the triangle midsegment theorem, if a line segment joins two sides of a triangle at their midpoints, then that line segment is parallel to the third side of that triangle and is half as long as that third side. So we can say that $\overline{DE} \parallel \overline{BC}$, and $BC$ is two times as long as $DE$.
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