Problem
GEO-B1-M04-P008 One Right Angle
#8
★★☆☆☆ Level 2 of 5
Prove that if one angle of a parallelogram is right, then the parallelogram is a rectangle.
In a parallelogram, adjacent angles are supplementary and opposite angles are equal.
Let \(\angle A=90^\circ\) in parallelogram \(ABCD\). Since \(AD\parallel BC\), angles \(A\) and \(B\) are same-side interior angles, so \(\angle A+\angle B=180^\circ\). Hence \(\angle B=90^\circ\). Opposite angles of a parallelogram are equal, so \(\angle C=90^\circ\) and \(\angle D=90^\circ\). All angles are right, so it is a rectangle.
Reinforces the connection between parallel lines and special parallelograms.