Question

write an equation to show the relationship between ( sl ) and the bases of the trapezoid.
xztp is a trapezoid where ( xp parallel zt ). ( sl ) is a midsegment of xztp and ( xs = 7 ), ( lt = 6 ), ( sl = 10 ), ( tz = 2x - 4 ), and ( xp = x - 3 ).
options:
( xp + zt )
( (xp + zt) + 2 )
( xp = zt )
( 2(xp + zt) )
( (xp + zt)/2 )

Explanation:

Step1: Recall trapezoid midsegment rule

The midsegment of a trapezoid is equal to half the sum of the lengths of its two parallel bases.

Step2: Match variables to the rule

Here, the midsegment is $SL$, and the two parallel bases are $XP$ and $ZT$. Substitute into the rule:
$SL = \frac{XP + ZT}{2}$
This can also be rewritten as $2SL = XP + ZT$, but the core relationship is the midsegment equals the average of the two bases.

Answer:

$\boldsymbol{(XP + ZT)/2}$ (corresponding to the last option: $\boldsymbol{(XP + ZT)/2}$)