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: 26


A triangle cannot have these lengths for its sides.

Work Step by Step

Using the Triangle Inequality Theorem, we need to see if the sum of each of the combinations of two sides is greater than the other side: $5 + 9 > 4$ --> This statement is true. $4 + 9 > 5$ --> This statement is true. $4 + 5 > 9$ --> This statement is false. A triangle cannot have these lengths for its sides because two of the sides added together are not greater than the third side.
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