The quadrilateral ABCD with vertices A(4, 4), B(5, 8), C(8, 8), and D(8, 5) can be classified as a trapezoid and more specifically, a right trapezoid. Here’s why:
1. **Understanding the Vertices**: The vertices of the quadrilateral are A(4, 4), B(5, 8), C(8, 8), and D(8, 5). When we plot these points on a Cartesian coordinate system, we can visualize the shape clearly.
2. **Finding the Slope of Each Side**: To classify the quadrilateral properly, we need to determine the slopes of each side. Here’s a quick breakdown:
- **Slope of AB:** Between points A and B, the slope is (y2 – y1)/(x2 – x1) = (8 – 4)/(5 – 4) = 4.
- **Slope of BC:** Between points B and C, the slope is (8 – 8)/(8 – 5) = 0, which indicates that BC is horizontal.
- **Slope of CD:** Between points C and D, the slope is (5 – 8)/(8 – 8) = Undefined, indicating that CD is vertical.
- **Slope of DA:** Between points D and A, the slope is (4 – 5)/(4 – 8) = 1/4.
3. **Analyzing the Shape**: From our slope calculations, we notice that sides AB and CD are not parallel, while BC is horizontal and CD is vertical. This configuration indicates that we have at least one pair of parallel sides, which is characteristic of a trapezoid.
4. **Identifying Right Angles**: Furthermore, since BC is horizontal and CD is vertical, the angle formed between these lines (angle BCD) is a right angle. This right angle confirms that ABCD is a right trapezoid.
In conclusion, the most precise term for quadrilateral ABCD is a right trapezoid due to the nature of its sides and the presence of a right angle. Understanding the properties of trapezoids not only aids in classification but also enriches our spatial reasoning and geometry skills.