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Interior angles of a parallelogram
 
Try this Drag the orange dots on each vertex to reshape the parallelogram. Notice the behavior of the four interior angles.

In any polygon, the interior angles have certain properties. See Interior angles of a polygon. A parallelogram however has some additional properties.

1. Opposite angles are congruent

As you drag any vertex in the parallelogram above, note that the opposite angles are congruent (equal in measure). Note for example that the angles ∠ABD and ∠ACD are always equal no matter what you do.

2. Consecutive angles are supplementary

If you start at any angle, and go around the parallelogram in either direction, each pair of angles you encounter always are supplementary - they add to 180°.

For example m∠ABD + m∠BDC =180°.

This is a result of the line BD being a transversal of the parallel lines AB and CD. Drag any orange dot in the figure above to reshape the parallelogram, and note that this is always true.

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Other polygon topics

General

Types of polygon

Area of various polygon types

Perimeter of various polygon types

Angles associated with polygons

Named polygons