Geometry: Common Core (15th Edition)

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

Chapter 5 - Relationships Within Triangles - 5-6 Inequalities in One Triangle - Practice and Problem-Solving Exercises - Page 329: 9


$\angle M < \angle L < \angle K $

Work Step by Step

Theorem 5-11 states that the longer side of a triangle is opposite the largest angle. So let's list the lengths of the sides first in order from smallest to largest: $2.7 < 4.3 < 5.8$ Now, let's list the sides of the triangle corresponding to these lengths in order from smallest to largest: $\overline{LK} < \overline{KM} < \overline{LM}$ We now look at the angles opposite these sides to place them in order from the smallest angle (which is opposite the smallest side) to the largest angle (which is opposite the largest side): $\angle M < \angle L < \angle K $
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