Question 1: In a parallelogram, one interior angle measures 75°. Calculate the measures of the adjacent angles.

Answer: 105

Question 2: Construct a parallelogram with sides of lengths 8 cm and 5 cm. Mark the angles to show that opposite angles are equal.

Answer: Constructed parallelogram with opposite angles equal

Question 3: A parallelogram has sides of 10 cm and 6 cm. If one height (altitude) corresponding to the 10 cm side is 4 cm, find the area of the parallelogram.

Answer: 40

Question 4: Fluency & Practice: Given a parallelogram with sides 7 cm and 9 cm, and an angle of 60°, calculate the length of the diagonal using the Law of Cosines.

Answer: 10.82

Question 5: Problem Solving & Reasoning: Two sides of a parallelogram are 12 cm and 8 cm. The diagonals are 15 cm and 10 cm. Determine if these measurements are possible and explain your reasoning.

Answer: Possible; based on the parallelogram law and diagonal properties

Question 6: A rectangle is a special case of a parallelogram. True or False? Justify your answer.

Answer: True

Question 7: Calculate the length of the side of a parallelogram if its perimeter is 48 cm, and the lengths of adjacent sides are 14 cm and x cm.

Answer: 10

Question 8: Construct a parallelogram where the sides are 9 cm and 4 cm, and the height corresponding to the 9 cm side is 3 cm. Calculate the area.

Answer: 27

Question 9: A parallelogram has angles of 70° and 110°. Find the sum of the two non-adjacent interior angles.

Answer: 180

Question 10: Error Analysis: A student claims that all parallelograms have right angles. Identify and correct this misconception.

Answer: Not all parallelograms have right angles; for example, rhombuses and general parallelograms can have oblique angles.

Question 11: Challenge & Extension: Prove that the diagonals of a parallelogram bisect each other using coordinate geometry.

Answer: Diagonals bisect each other; midpoint of one diagonal equals midpoint of the other.