Question

The quadrilateral formed by joining the mid-point of a quadrilateral ABCD, taken in order is a rectangle, if ______.

पर्याय

• ABCD is a rectangle

• ABCD is a parallelogram

• AC ⊥ BD

• AC = BD

Answer 1

The quadrilateral formed by joining the mid-point of a quadrilateral ABCD, taken in order is a rectangle, if AC ⊥ BD.

Explanation:

By the midpoint Varignon theorem, the quadrilateral formed by joining the midpoints is a parallelogram whose adjacent sides are parallel to the diagonals AC and BD and have half their lengths.

Hence, those adjacent sides are perpendicular exactly when AC is perpendicular to BD, so the midpoint-quadrilateral is a rectangle.