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.

Tags

CCSS.3.G.A.1

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.

Tags

CCSS.HSG.CO.C.11

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.

Tags

CCSS.HSG.C.A.3

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.

Tags

CCSS.HSG.C.A.3

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.

Tags

CCSS.HSG.C.A.3

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.

Tags

CCSS.HSG.CO.C.11

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.

Tags

CCSS.HSG.CO.C.11

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.

Tags

CCSS.HSG.CO.C.11

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.

Tags

CCSS.HSG.C.A.3