Geometry: Common Core (15th Edition)

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

Chapter 6 - Polygons and Quadrilaterals - 6-6 Trapezoids and Kites - Practice and Problem-Solving Exercises - Page 395: 30


$x = 1$

Work Step by Step

Theorem 6-20 states that in an isosceles trapezoid, diagonals are congruent. Let's set the two diagonals equal to one another: $QS = RP$ Let's plug in the expressions for each diagonal: $x + 5 = 3x + 3$ Subtract $5$ from each side of the equation to move constants to the right side of the equation: $x = 3x - 2$ Subtract $3x$ from each side of the equation to move the variable to the left side of the equation: $-2x = -2$ Divide each side by $-2$ to solve for $x$: $x = 1$
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