figure abcd is a parallelogram. two trapezoids are created using line segment xy such that $\overline{ax} \cong \overline{cy}$. what is true about the areas of the trapezoids? $\bigcirc$ each area is equal to half of the area of abcd. $\bigcirc$ the area of axyd is less than the area of bxyc. $\bigcirc$ the area of axyd is greater than the area of bxyc. $\bigcirc$ each area is equal to the area of abcd.

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# Brief Explanations:
1. Recall the properties of a parallelogram: In a parallelogram $ABCD$, $AB = CD$ and $AB\parallel CD$. The area of a parallelogram is given by $A = base\times height$.
2. Analyze the trapezoids: Trapezoid $AXYD$ and trapezoid $BXYC$ are formed by the line segment $XY$ such that $\overline{AX}\cong\overline{CY}$. Since $AB = CD$ (opposite sides of a parallelogram) and $AX = CY$, we can show that $XD=AB - AX$ and $BY = CD - CY$, so $XD = BY$.
3. The height of both trapezoids is the same as the height of the parallelogram (because the trapezoids are between the same parallel lines $AB$ and $CD$).
4. The area of a trapezoid is given by $A=\frac{(a + b)}{2}\times h$, where $a$ and $b$ are the lengths of the parallel sides and $h$ is the height. For trapezoid $AXYD$, the parallel sides are $AX$ and $XD$, and for trapezoid $BXYC$, the parallel sides are $CY$ and $BY$. Since $AX = CY$ and $XD = BY$, and the height $h$ is the same for both trapezoids, we can also think about the area of the parallelogram. The sum of the areas of the two trapezoids is equal to the area of the parallelogram $ABCD$. Also, because of the congruence of $AX$ and $CY$ and the equality of $XD$ and $BY$, the areas of the two trapezoids are equal. So each area is equal to half of the area of $ABCD$.
# Answer:
A. Each area is equal to half of the area of $ABCD$

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