Final answer:
To find the slope of each side of a quadrilateral and determine if it is a parallelogram, use the formula for the slope of a line and compare the slopes of opposite sides.
Step-by-step explanation:
To determine if a quadrilateral is a parallelogram, we need to find the slopes of its sides. The slope of a line can be calculated by finding the rise over run between two points on the line. Let's denote the coordinates of the vertices of the quadrilateral as A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4). To find the slope of AB, we use the formula:
slope of AB = (y2 - y1) / (x2 - x1)
We repeat this process to find the slopes of the other sides: BC, CD, and DA. If the slopes of opposite sides are equal, then the quadrilateral is a parallelogram. Otherwise, it is not.