10 1 point
Quadrilateral EFGH has vertices E(-5, 1), F(-1, 6), G(4, 1), and H(-1,-4). Which type of quadrilateral best describes EFGH?
rectangle
parallelogram
trapezoid
kite
Quadrilateral EFGH can be identified as a parallelogram based on the information given about its vertices. Here's how we can determine this:
1. **Definition of a Parallelogram:** A parallelogram is a four-sided figure where both pairs of opposite sides are parallel and equal in length.
2. **Analyzing the Given Vertices:**
- Side EF is parallel to side GH (slope EF = slope GH) and they are equal in length.
- Side FG is parallel to side EH (slope FG = slope EH) and they are equal in length.
3. **Verifying Parallelogram Properties:**
- Opposite sides EF and GH are parallel and equal.
- Opposite sides FG and EH are parallel and equal.
Therefore, based on the properties of a parallelogram, it can be concluded that quadrilateral EFGH is best described as a parallelogram.
