Exploring Parallelograms

What are the properties of a parallelogram?

• Opposite sides are equal, opposite angles are equal, adjacent angles are supplementary, and diagonals bisect each other.

• Diagonals are equal in length

• All sides are equal in length

• All angles are right angles

How do you prove that a quadrilateral is a parallelogram?

• A quadrilateral is a parallelogram if all sides are equal.

• A quadrilateral is a parallelogram if the diagonals are equal.

• A quadrilateral is a parallelogram if both pairs of opposite sides are equal, both pairs of opposite angles are equal, the diagonals bisect each other, or one pair of opposite sides is both equal and parallel.

If one angle of a parallelogram is 70 degrees, what are the measures of the other angles?

• 70 degrees, 110 degrees, 70 degrees, 110 degrees

• 90 degrees, 90 degrees, 90 degrees, 90 degrees

• 80 degrees, 100 degrees, 80 degrees, 100 degrees

• 60 degrees, 120 degrees, 60 degrees, 120 degrees

What is the relationship between the opposite sides of a parallelogram?

• Opposite sides of a parallelogram are equal in length and parallel.

• Opposite sides of a parallelogram are always different lengths.

• Opposite sides of a parallelogram are perpendicular to each other.

• Opposite sides of a parallelogram are not parallel.

How do the diagonals of a parallelogram behave?

• The diagonals of a parallelogram are perpendicular to each other.

• The diagonals of a parallelogram are equal in length.

• The diagonals of a parallelogram bisect each other.

• The diagonals of a parallelogram do not intersect.

If the diagonals of a quadrilateral bisect each other, what can you conclude about the quadrilateral?

• The quadrilateral is a rhombus.

• The quadrilateral is a trapezoid.

• The quadrilateral is a rectangle.

• The quadrilateral is a parallelogram.

What is the formula for the area of a parallelogram?

• Area = 2 × (base + height)

• Area = base × base

• Area = base + height

• Area = base × height

How can you determine if a quadrilateral is a parallelogram using its sides?

• A quadrilateral is a parallelogram if at least one pair of opposite angles are equal.

• A quadrilateral is a parallelogram if all four sides are equal in length.

• A quadrilateral is a parallelogram if both pairs of opposite sides are equal in length.

• A quadrilateral is a parallelogram if the diagonals are equal in length.

What is the significance of the opposite angles in a parallelogram?

• Opposite angles in a parallelogram are supplementary.

• Opposite angles in a parallelogram are always acute.

• Opposite angles in a parallelogram are equal.

• Opposite angles in a parallelogram are complementary.

If two sides of a quadrilateral are parallel and equal in length, what can you say about the quadrilateral?

• The quadrilateral is a rectangle.

• The quadrilateral is a rhombus.

• The quadrilateral is an isosceles trapezoid.

• The quadrilateral is a square.