# Parallelograms

Warmup

Activity #1

Investigate the Different Types of Parallelograms.

Parallelograms are classified into three main types: square, rectangle, and rhombus, and each of them has its own unique properties.

• Check the two boxes in the figure below to see the angles and side lengths.â€‹
• Drag the blue points around to see different types of a parallelogram.
• Turn on the grid for a detail representation.

Activity #2

Investigate the Properties of a Parallelogram.

A parallelogram with all four sides equal in length is called a rhombus. If all four angles of a parallelogram are equal, then each angle equals 90Â°, and the figure is a RECTANGLE. A parallelogram that is both equilateral and equiangular is a SQUARE.

• Move the slider slowly to the right and observe the figure.â€‹

Activity #3

Investigate if a Figure is a Parallelogram.

An examination of alternate angles across parallel lines quickly shows that opposite angles in a parallelogram are equal and that adjacent angles are supplementary, that is, sum to 180Â°. The parallelogram is the only quadrilateral with this property. The DIAGONALs of a parallelogram bisect one another, and again the parallelogram is the only quadrilateral that has this property.

• Move the points in the graph below so that the figure forms a parallelogram.â€‹
• Use any 1 or more of the provided tools to verify that your quadrilateral is indeed a parallelogram.