## Geometry: Common Core (15th Edition)

$EF = 1$ $HG = 11$ $CD = 6$
According to the trapezoid midsegment theorem, in a quadrilateral that is a trapezoid, the midsegment is parallel to the bases and is half the sum of the base lengths. Let's set up the equation to find the value of $x$: $2x + 4 = \frac{1}{2}[(x) + (4x + 7)]$ Evaluate parentheses first: $2x + 4 = \frac{1}{2}(5x + 7)$ Divide both sides by $\frac{1}{2}$ to get rid of the fraction. $2(2x + 4) = 5x + 7$ $4x + 8 = 5x + 7$ Subtract $5x$ from both sides of the equation to move variable terms to the left side of the equation: $-x + 8 = 7$ Subtract $8$ from both sides of the equation to move constants to the right side of the equation: $-x = -1$ Divide both sides by $-1$ to solve for $x$: $x = 1$ Now we plug $1$ in for $x$ $EF = x$ Let's substitute $1$ for $x$: $EF = 1$ Let's look at the expression for the longer base: $HG = 4x + 7$ Substitute $1$ for $x$ $HG = 4(1) + 7$ Multiply first, according to order of operations: $HG = 4 + 7$ Add to solve: $HG = 11$ Finally, let's look at the expression for the midsegment: $CD = 2x + 4$ Substitute $1$ for $x$: $CD = 2(1) + 4$ Multiply first, according to order of operations: $CD = 2 + 4$ Add to solve: $CD = 6$