Question 1: A parallelogram has sides measuring 8 cm and 5 cm. What is the perimeter of the parallelogram?

Answer: 26

Question 2: In a parallelogram, opposite angles are equal. If one angle measures 70°, what is the measure of the adjacent angle?

Answer: 110

Question 3: Construct a parallelogram with a base of 6 units and a height of 4 units. Calculate its area.

Answer: 24

Question 4: A diagram shows a four-sided figure with opposite sides parallel and equal, but the angles are not all 90°. Is this figure necessarily a parallelogram? Explain your answer.

Answer: Yes, because opposite sides are parallel and equal, which defines a parallelogram.

Question 5: Identify the mistake in the following statement: 'A quadrilateral with equal sides and right angles must be a rectangle, so it cannot be a parallelogram.'

Answer: The mistake is the assumption that all parallelograms with right angles are rectangles, but squares are also parallelograms with right angles and equal sides.

Question 6: Calculate the length of the diagonal of a parallelogram with sides 7 cm and 24 cm, where the included angle is 60°.

Answer: 25

Question 7: Two students claim that all parallelograms have four right angles. Use properties of parallelograms to explain whether this is true or false.

Answer: False. Only rectangles have four right angles; parallelograms can have angles that are not 90°.

Question 8: Show how to construct a parallelogram on the grid with a base of 5 units. Use the grid to draw and label your figure.

Answer: Student's drawing on grid, with labeled sides.

Question 9: In the diagram, a parallelogram has sides of 9 units and 12 units. The diagonals intersect at point O. If the diagonals bisect each other, what is the length of each diagonal if they intersect at a point 8 units from one vertex?

Answer: 20

Question 10: A student incorrectly states that all parallelograms are rhombuses. Identify and explain the misconception.

Answer: The misconception is that all parallelograms are rhombuses. In reality, parallelograms have opposite sides parallel and equal, but a rhombus has all sides equal. Not all parallelograms are rhombuses.

Question 11: Using the properties of a parallelogram, prove that the diagonals bisect each other.

Answer: Diagonals bisect because in a parallelogram, opposite sides are equal and parallel, which leads to each diagonal being divided into two equal segments at the point of intersection.