Geometry: Common Core (15th Edition)

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

Chapter 2 - Reasoning and Proof - 2-2 Conditional Statements - Apply What You've Learned: c

Answer

Converse: If $a+d=b+c$, then a, b, c and d form a 2-by-2 calendar square. Inverse: If a, b, c and d do not form a 2-by-2 calendar square, then $a+d\ne b+c$. The same counterexamples can be used to show that the converse and inverse are false. Four consecutive squares lettered a-d is a counterexample. (i.e. a=1, b=2, c=3, d=4) Such numbers satisfy the equality but are not a calendar square. Four consecutive even numbered squares lettered a-d is a counterexample. (i.e. a=2, b=4, c=6, d=8) Such numbers satisfy the equality but are not a calendar square.

Work Step by Step

The inverse and converse are false statements, so counterexamples can be found.
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