Geometry: Common Core (15th Edition)

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

Chapter 1 - Tools of Geometry - 1-3 Measuring Segments - Practice and Problem-Solving Exercises - Page 25: 39


y=15 AC is 24 DC is 12

Work Step by Step

The diagram shows that $\overline{AD}$ and $\overline{DC}$ are congruent, so AD=DC. $AD+DC=AC\longrightarrow$ Segment Addition Postulate $AD+AD=AC\longrightarrow$ substitute $12+12=4y-36\longrightarrow$ substitute $24=4y-36\longrightarrow$ simplify $24+36=4y-36+36\longrightarrow$ add 36 to each side $60=4y\longrightarrow$ simplify $60\div4=4y\div4\longrightarrow$ divide each side by 4 $15=y\longrightarrow$ simplify AC=$4y-36=4(15)-36=60-36=24$ DC=AD=$12$
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