Lesson Worksheet: Properties of Parallelograms Mathematics

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:

Given that 𝐴𝐵𝐶𝐷 is a parallelogram and 𝑚∠𝐶=68∘, find 𝑚∠𝐴.

Q6:

In the figure below, given that 𝐴𝐵𝐶𝐷 is a parallelogram, determine 𝑚∠𝐻𝐷𝐶.

Q7:

In the figure below, given that 𝐴𝐵𝐶𝐷 is a parallelogram, find 𝑚∠𝐴.

Q8:

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)

Q9:

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.

Q10:

In the parallelogram 𝐸𝐹𝐺𝐻, 𝑚∠𝐸𝐻𝐺=(3𝑥+19)∘, 𝑚∠𝐻𝐺𝐹=(2𝑥+6)∘, and 𝑚∠𝐹𝐸𝐻=(2𝑦)∘. Find the values of 𝑥 and 𝑦.

  • A𝑥=31, 𝑦=34
  • B𝑥=13, 𝑦=100
  • C𝑥=13, 𝑦=29
  • D𝑥=31, 𝑦=100
  • E𝑥=13, 𝑦=10

Q11:

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

Q12:

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

Q13:

Find 𝑚∠𝐷.

Q14:

In the figure, 𝐴𝐵𝐶𝐷 and 𝐶𝐵𝐻𝑂 are parallelograms. Find 𝑚∠𝐴𝐵𝐻.

Q15:

Given that 𝐴𝐵𝐶𝐷 is a parallelogram, find the area of triangle 𝐴𝐵𝑀.

Q16:

𝐴𝐵𝐶𝐷 is a parallelogram, where the coordinates of the points 𝐴, 𝐵, and 𝐶 are (4,−9), (3,2), and (5,5), respectively. Find the coordinates of the vertex 𝐷.

  • A(6,−6)
  • B92,−2
  • C(2,−12)
  • D(3,−2)

Q17:

𝐴𝐵𝐶𝐷 is a parallelogram, and 𝑚∠𝐷𝐴𝐶=5𝑥∘, 𝑚∠𝐵𝐴𝐶=3𝑥∘, and 𝑚∠𝐴𝐵𝐶=4𝑥∘. Determine 𝑚∠𝐵𝐶𝐷 and 𝑚∠𝐴𝐷𝐶.

  • A60∘, 120∘
  • B115∘, 65∘
  • C120∘, 60∘
  • D60∘,30∘

Q18:

Find 𝑚∠𝐶𝐵𝐷.

Q19:

In parallelogram 𝐴𝐵𝐶𝐷, suppose 𝑚∠𝐴+𝑚∠𝐶=222∘. What is 𝑚∠𝐵?

Q20:

Given that 𝐴𝐵𝐶𝐷 is a parallelogram, find 𝑥.

Q21:

In parallelogram 𝐴𝐵𝐶𝐷, suppose 𝐷𝑋=44 and 𝐵𝑌=53. How are the lengths 𝐴𝑋+𝐴𝐵 and 𝐶𝑌+𝐶𝐷 related?

  • A𝐴𝑋+𝐴𝐵=𝐶𝑌+𝐶𝐷
  • B𝐴𝑋+𝐴𝐵>𝐶𝑌+𝐶𝐷
  • C𝐴𝑋+𝐴𝐵<𝐶𝑌+𝐶𝐷

Q22:

How many altitudes are there in a parallelogram?

Q23:

Which of the following are a base and its corresponding altitude in the given parallelogram?

  • Abase: 𝑂𝐷, altitude: 𝑂𝑌
  • Bbase: 𝑂𝐷, altitude: 𝐸𝐻
  • Cbase: 𝑂𝑌, altitude: 𝐸𝐻
  • Dbase: 𝑂𝐷, altitude: 𝐷𝑀

Q24:

Which of the following statements is not true?

  • AOpposite sides in a parallelogram are parallel.
  • BRhombuses have four congruent sides.
  • CParallelograms have exactly one pair of parallel sides.
  • DSquares have four congruent angles and sides.
  • ERectangles have four right angles.

Q25:

True or False: In a parallelogram, there is a pair of opposite sides that do not have to be parallel.

  • ATrue
  • BFalse

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