Lesson Worksheet: Properties of Parallelograms

In this worksheet, we will practice determining whether a quadrilateral is a parallelogram or not and using the properties of parallelograms to find unknown angles or lengths.

Q1:

True or False: In a parallelogram, opposite sides are parallel and equal in length.

  • ATrue
  • BFalse

Q2:

True or False: All parallelograms are regular polygons.

  • ATrue
  • BFalse

Q3:

Which of the following statements correctly describes a property of the given shape?

  • AIt is equilateral.
  • BIt contains 2 pairs of perpendicular sides.
  • CIt has 4 angles equal in measure.
  • DIt has 2 sets of perpendicular and parallel sides.
  • EIt contains 2 pairs of parallel sides.

Q4:

Find the lengths of 𝐶𝐷 and 𝐷𝐴.

  • A𝐶𝐷=15cm, 𝐷𝐴=13cm
  • B𝐶𝐷=13cm, 𝐷𝐴=15cm
  • C𝐶𝐷=15cm, 𝐷𝐴=28cm
  • D𝐶𝐷=28cm, 𝐷𝐴=13cm

Q5:

In the figure below, given that 𝐴𝐵𝐶𝐷 is a parallelogram, determine 𝑚𝐻𝐷𝐶.

Q6:

In the figure below, given that 𝐴𝐵𝐶𝐷 is a parallelogram, find 𝑚𝐴.

Q7:

𝐴𝐵𝐶𝐷 is a parallelogram such that 𝐴(3,4), 𝐵(0,4), and 𝐶(2,2). Determine the coordinates of vertex 𝐷.

  • A(7,3)
  • B(6,1)
  • C(1,6)
  • D(1,2)
  • E(5,2)

Q8:

Which of the following statements must be true about a parallelogram?

  • AIt has one pair of parallel sides.
  • BIt has four congruent sides.
  • CIt has four sides of equal length.
  • DIt has four right angles.
  • EIt has two pairs of parallel opposite sides.

Q9:

What is the sum of the measures of any two consecutive angles in a parallelogram?

Q10:

In the following figure 𝐴𝐵𝐶𝐷 is a parallelogram. What is the measure of 𝐴?

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