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 neither a parallelogram nor a rectangle.
b. the quadrilateral is both a parallelogram and a rectangle.
c. the quadrilateral is a rectangle, but not a parallelogram.
d. the quadrilateral is a parallelogram, but not a rectangle.

Explanation:

Step1: Recall the properties of parallelograms and rectangles

A parallelogram has opposite sides equal. A rectangle is a parallelogram with all angles equal to \(90^{\circ}\) (and also has opposite sides equal). Given \(EF = 8\) units, \(FG=15\) units, \(GH = 8\) units, \(EH=15\) units.

Step2: Check the condition for a parallelogram

Since \(EF = GH\) (\(EF = 8\), \(GH = 8\)) and \(FG=EH\) (\(FG = 15\), \(EH = 15\)), by the property that if in a quadrilateral opposite sides are equal, then the quadrilateral is a parallelogram.

Step3: Check the condition for a rectangle

To be a rectangle, we need information about the angles (or about the diagonals being equal). We are not given any information about the angles (or about the lengths of the diagonals \(EG\) and \(FH\)). So, we cannot conclude it is a rectangle.

Answer:

D. The quadrilateral is a parallelogram, but not a rectangle.