Geometry: Common Core (15th Edition)

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

Chapter 6 - Polygons and Quadrilaterals - 6-3 Proving That a Quadrilateral Is a Parallelogram - Practice and Problem-Solving Exercises - Page 372: 10


$x = \frac{5}{3}$

Work Step by Step

Parallelograms have opposite sides that are congruent. In order for $ABCD$ to be a parallelogram, we must have $AD$ and $BC$ equal to one another. $AD = BC$ Let's plug in what we are given in the diagram: $3x + 1 = 6x - 4$ Subtract $1$ from each side of the equation to isolate variables to one side of the equation: $3x = 6x - 5$ Subtract $6x$ from each side of the equation to isolate the variable to the left side of the equation: $-3x = -5$ Divide each side of the equation by $-3$ to solve for $x$: $x = \frac{5}{3}$
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