Properties of Parallelograms

Front

What is a parallelogram?

Back

A parallelogram is a quadrilateral with opposite sides that are both parallel and equal in length.

Front

What are the properties of a parallelogram?

Back

1. Opposite sides are equal in length. 2. Opposite angles are equal. 3. The diagonals bisect each other. 4. Consecutive angles are supplementary.

Front

How can you prove that a quadrilateral is a parallelogram using opposite sides?

Back

If both pairs of opposite sides are equal in length, then the quadrilateral is a parallelogram.

Front

What does it mean for diagonals to bisect each other in a parallelogram?

Back

It means that the diagonals of the parallelogram intersect at their midpoints, dividing each diagonal into two equal segments.

Front

What is the significance of opposite angles in a parallelogram?

Back

In a parallelogram, opposite angles are equal, which helps in proving that a quadrilateral is a parallelogram.

Front

What is the relationship between consecutive angles in a parallelogram?

Back

Consecutive angles in a parallelogram are supplementary, meaning they add up to 180 degrees.

Front

What theorem states that if one pair of opposite sides is both parallel and equal, the quadrilateral is a parallelogram?

Back

The theorem states that if one pair of opposite sides is both parallel and congruent, then the quadrilateral is a parallelogram.

Front

How can you determine if a quadrilateral is not a parallelogram?

Back

If not all pairs of opposite sides are equal or parallel, or if the diagonals do not bisect each other, then it is not a parallelogram.

Front

What is the converse of the property of diagonals bisecting each other?

Back

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Front

What is the relationship between the angles of a parallelogram?

Back

The sum of the interior angles of a parallelogram is 360 degrees, and each pair of opposite angles is equal.