Answer
$HG = 2$
$EF = 8$
$CD = 5$
Work Step by Step
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 $x$:
$x = \frac{1}{2}[(x - 3) + (2x - 2)]$
Evaluate parentheses first:
$x = \frac{1}{2}(3x - 5)$
Divide both sides by $\frac{1}{2}$ to get rid of the fraction.
$2(x) = 3x - 5$
Subtract $3x$ from both sides of the equation to move variable terms to the left side of the equation:
$-x = -5$
Divide both sides by $-1$ to solve for $x$:
$x = 5$
$HG = x - 3$
Let's substitute $5$ for $x$:
$HG = 5 - 3$
Subtract to solve:
$HG = 2$
Let's look at the expression for the longer base:
$EF = 2x - 2$
Substitute $5$ for $x$
$EF = 2(5) - 2$
Multiply first, according to order of operations:
$EF = 10 - 2$
Subtract to solve:
$EF = 8$
Finally, let's look at the expression for the midsegment:
$CD = x$
Substitute $5$ for $x$:
$CD = 5$
