Discovering Parallelogram Properties: Angles & Coordinates

A parallelogram has vertices at A(1, 2), B(5, 2), C(6, 5), and D(2, 5). Calculate the lengths of the sides AB and AD. Are they equal?

• AB = 3, AD = $\sqrt{10}$, equal.

• AB = 4, AD = 4, equal.

• AB = 5, AD = $\sqrt{5}$, not equal.

• AB = 4, AD = \sqrt{10}, not equal.

In a parallelogram, the angles at vertices A and C are supplementary. If angle A measures 70 degrees, what is the measure of angle C?

• 80 degrees

• 70 degrees

• 60 degrees

• 90 degrees

A parallelogram is inscribed in a park with corners at (0, 0), (4, 0), (5, 3), and (1, 3). What is the area of the park?

• 8

• 10

• 12

• 15

Given a parallelogram with vertices at P(2, 3), Q(6, 3), R(7, 6), and S(3, 6), find the coordinates of the midpoint of diagonal PR.

• (5, 5)

• (4.5, 4.5)

• (6, 4)

• (3, 4)

A parallelogram has one angle measuring 45 degrees. What are the measures of the other three angles?

• 60 degrees, 60 degrees, 60 degrees

• 45 degrees, 135 degrees, 135 degrees

• 30 degrees, 30 degrees, 120 degrees

• 90 degrees, 90 degrees, 90 degrees

A parallelogram has vertices at (2, 1), (6, 1), (7, 4), and (3, 4). Determine the slope of the sides AB and CD. Are they parallel?

• Yes, the slopes of sides AB and CD are equal, so they are parallel.

• No, the slopes of sides AB and CD are both zero, so they are not parallel.

• Yes, the slopes of sides AB and CD are undefined, making them parallel.

• No, the slopes of sides AB and CD are different, so they are not parallel.

In a parallelogram, the diagonals bisect each other. If one diagonal connects points (2, 3) and (8, 3), where does the other diagonal intersect?

• (6, 3)

• (4, 3)

• (5, 4)

• (5, 3)

A parallelogram has a base of 10 cm and a height of 5 cm. What is its area? How would the area change if the height is doubled?

• The area is 60 cm². If the height is doubled, the area becomes 120 cm².

• The area is 25 cm². If the height is doubled, the area becomes 75 cm².

• The area is 50 cm². If the height is doubled, the area becomes 100 cm².

• The area is 40 cm². If the height is doubled, the area becomes 80 cm².

If a parallelogram has vertices at (1, 2), (4, 5), (7, 2), and (4, -1), calculate the lengths of the diagonals. Are they equal?

• The lengths of the diagonals are 6 and 4, and they are not equal.

• The lengths of the diagonals are both 6, and they are equal.

• The lengths of the diagonals are both 8, and they are equal.

• The lengths of the diagonals are 5 and 7, and they are not equal.

A parallelogram is used as a design for a garden. If the lengths of the sides are 8 m and 6 m, and the angle between them is 60 degrees, calculate the area of the garden.

• 12√3 m²

• 36 m²

• 24√3 m²

• 48 m²