Geometry: Common Core (15th Edition)

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

Chapter 6 - Polygons and Quadrilaterals - Chapter Test - Page 425: 8

Answer

$x = 6$ $y = 5$

Work Step by Step

The diagonals of a parallelogram bisect one another; therefore, we can set the two bisected segments of each diagonal equal to one another. Let's start with the diagonal in which the segments have the same variable: $4x - 4 = 3x + 2$ Subtract $3x$ from each side of the equation to move variables to the left side of the equation: $x - 4 = 2$ Add $4$ to each side of the equation to solve for $x$: $x = 6$ Now, we can set the other two segments on the other diagonal equal to one another: $2y + 2 = 2x$ Substitute $6$ for $x$: $2y + 2 = 2(6)$ Multiply first, according to order of operations: $2y + 2 = 12$ Subtract $2$ from each side of the equation to move constants to the right side of the equation: $2y = 10$ Divide both sides of the equation by $2$ to solve for $y$: $y = 5$
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