Parallelogram Properties

What is the definition of a parallelogram?

• A shape with four equal sides and four right angles.

• A quadrilateral with opposite sides that are parallel and equal in length.

• A triangle with two equal sides.

• A polygon with all sides of different lengths.

How can you use the properties of a parallelogram to find missing side lengths?

• Use the equations derived from the properties (e.g., opposite sides are equal) to set up and solve for the missing lengths.

• Add the lengths of all sides to find the missing length.

• Use the Pythagorean theorem to calculate the missing side lengths.

• Subtract the lengths of adjacent sides to find the missing length.

In a parallelogram, if one angle measures 60 degrees, what are the measures of the other angles?

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

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

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

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

If two angles of a parallelogram are 70 degrees, what are the measures of the other two angles?

• 90 degrees each

• 100 degrees each

• 110 degrees each

• 120 degrees each

How can you determine if a quadrilateral is a parallelogram?

• Both pairs of opposite sides are equal.

• All angles are right angles.

• The diagonals are equal in length.

• One pair of opposite sides is both equal and parallel.

How do you prove that a quadrilateral is a parallelogram using angle properties?

• If both pairs of opposite angles are equal, then the quadrilateral is a parallelogram.

• If one pair of opposite angles are equal, then the quadrilateral is a parallelogram.

• If the sum of the interior angles is 360 degrees, then the quadrilateral is a parallelogram.

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

If SV = x + 3 and VU = 2x - 1 in parallelogram STUV, how do you find x?

• Set the equations equal to each other since opposite sides are equal: x + 3 = 2x - 1, then solve for x.

• Add 1 to both sides of the equation: x + 4 = 2x.

• Subtract 3 from both sides of the equation: SV - 3 = VU.

• Multiply both sides of the equation by 2: 2(SV) = 2(VU).

What is the significance of opposite angles in a parallelogram?

• Opposite angles in a parallelogram are equal, which helps in solving for unknown angles.

• Opposite angles in a parallelogram are supplementary, adding up to 180 degrees.

• Opposite angles in a parallelogram are always acute angles.

• Opposite angles in a parallelogram are always right angles.

How do you solve for a variable in a parallelogram's side lengths?

• Set up equations based on the properties of parallelograms (e.g., opposite sides are equal) and solve for the variable.

• Use the Pythagorean theorem to find the length of the diagonal.

• Add the lengths of all sides and divide by four to find the average length.

• Multiply the lengths of the sides by two to find the perimeter.

What are the properties of a parallelogram?

• 1. Opposite sides are equal in length.

• 2. Opposite angles are equal.

• 3. The diagonals bisect each other.

• 4. All angles are right angles.