Answer
$AD = 4$
$BC = 14$
$EF = 9$
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 $x$:
$x = \frac{1}{2}[(2x - 4) + (x - 5)]$
Evaluate parentheses first:
$x = \frac{1}{2}(3x - 9)$
Divide both sides by $\frac{1}{2}$ to get rid of the fraction.
$2(x) = 3x - 9$
Subtract $3x$ from both sides of the equation to move variable terms to the left side of the equation:
$-x = -9$
Divide both sides by $-1$ to solve for $x$:
$x = 9$
Now we plug $9$ in for $x$:
$AD = x - 5$
Let's substitute $9$ for $x$:
$AD = 9 - 5$
Subtract to solve:
$AD = 4$
Let's look at the expression for the longer base:
$BC = 2x - 4$
Substitute $9$ for $x$:
$BC = 2(9) - 4$
Multiply first, according to order of operations:
$BC = 18 - 4$
Subtract to solve:
$BC = 14$
Finally, let's look at the expression for the midsegment:
$EF = x$
Substitute $9$ for $x$:
$EF = 9$
