Quadrilateral ABCD has congruent angles and opposite sides that are congruent. What classification can be given to ABCD? (5 points) Parallelogram Rectangle Rhombus Square
Accepted Solution
A:
All angles are congruent. The sum of the measures of the interior angles of a quadrilateral is 360. Since all angles are congruent, then each angle must measure 360/4 = 90. Every angle measures 90 degrees. The quadrilateral must be a rectangle. Is the quadrilateral also a square? We are told "opposite sides that are congruent." Since only opposites sides are congruent, and not all sides are congruent, then it is a rectangle, but not necessarily a square.