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: 40


ED is 10 DB is 10 EB is 20

Work Step by Step

The diagram shows $\overline{ED}$ and $\overline{DB}$ are congruent, so we obtain: ED=DB $x+4=3x-8\longrightarrow$ substitute and solve for x $x+4+8=3x-8+8\longrightarrow$ add 8 to each side $x+12=3x\longrightarrow$ simplify $x+12-x=3x-x\longrightarrow$ subtract x from each side $12=2x\longrightarrow$ simplify $12\div2=2x\div2\longrightarrow$ divide each side by 2 $6=x \longrightarrow$ simplify Substitute for x to find each length. ED=$x+4=6+4=10$ DB=$3x-8=3(6)-8=18-8=10$ Use the Segment Addition Postulate EB=ED+DB=$10+10=20$
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