Parallelograms and Rectangles
Use the following applet to prove the conjectures below.
• All rectangles are parallelograms.
• If a parallelogram has (at least) one right angle, then it is a rectangle.
• If a quadrilateral has 2 pairs of opposite sides that are congruent, then it is a parallelogram.
• If the diagonals of a quadrilateral both bisect each other, then the quadrilateral is a parallelogram.
• If the diagonals of a quadrilateral both bisect each other and they are perpendicular, then the quadrilateral is a rhombus.
Definition of a parallelogram:
a quadrilateral with two pairs of parallel opposite sides
Definition of a rectangle:
a quadrilateral with four right angles.