The problem states that in trapezoid $ABCD$, $PQ$ is the midsegment. Given that $DC = 18$ and $PQ = 14$, we need to find the length of $AB$.

1. Problem Description

The problem states that in trapezoid $ABCD$, $PQ$ is the midsegment. Given that $DC = 18$ and $PQ = 14$, we need to find the length of $AB$.

2. Solution Steps

The midsegment of a trapezoid is the segment that connects the midpoints of the non-parallel sides. The length of the midsegment is the average of the lengths of the two parallel sides. In trapezoid $ABCD$, $AB$ and $DC$ are the parallel sides, and $PQ$ is the midsegment. Therefore, we have the formula:

$PQ = \frac{AB + DC}{2}$

We are given that $PQ = 14$ and $DC = 18$. We need to find $AB$. Substitute the given values into the formula:

$14 = \frac{AB + 18}{2}$

Multiply both sides of the equation by 2:

$2 * 14 = AB + 18$

$28 = AB + 18$

Subtract 18 from both sides of the equation to solve for $AB$:

$AB = 28 - 18$

$AB = 10$

3. Final Answer

The length of $AB$ is

1

0. $AB = 10$