Question

quadrilateral efgh has the given measurements.

• ef = 8 units
• fg = 15 units
• gh = 8 units
• eh = 15 units
• fh = 17 units
• eg = 17 units

what conclusion can be made from the given information?
a. the quadrilateral is a parallelogram, but not a rectangle.
b. the quadrilateral is both a parallelogram and a rectangle.
c. the quadrilateral is neither a parallelogram nor a rectangle.
d. the quadrilateral is a rectangle, but not a parallelogram.

Explanation:

1. Check for Parallelogram: A parallelogram has opposite sides equal. Here, \(EF = GH = 8\) units and \(FG = EH = 15\) units, so opposite sides are equal, satisfying the parallelogram condition.
2. Check for Rectangle: A rectangle is a parallelogram with right angles (or diagonals equal). The diagonals \(FH = 17\) units and \(EG = 17\) units are equal. For a parallelogram, equal diagonals imply it is a rectangle (by the property that in a parallelogram, if diagonals are equal, it is a rectangle).

Thus, the quadrilateral is both a parallelogram and a rectangle.

Answer:

B. The quadrilateral is both a parallelogram and a rectangle.