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:

Is the following statement true or false? In a parallelogram, opposite sides are parallel and equal in length.

  • Atrue
  • Bfalse

Q2:

Determine whether this statement is 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.

  • A 𝐶 𝐷 = 1 5 c m , 𝐷 𝐴 = 1 3 c m
  • B 𝐶 𝐷 = 1 3 c m , 𝐷 𝐴 = 1 5 c m
  • C 𝐶 𝐷 = 1 5 c m , 𝐷 𝐴 = 2 8 c m
  • D 𝐶 𝐷 = 2 8 c m , 𝐷 𝐴 = 1 3 c m

Q5:

Given that 𝐴𝐵𝐶𝐷 is a parallelogram and 𝑚𝐶=68, find 𝑚𝐴.

Q6:

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

Q7:

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

Q8:

𝐴 𝐵 𝐶 𝐷 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, 𝑚𝐸𝐻𝐺=(3𝑥+19), 𝑚𝐻𝐺𝐹=(2𝑥+6), and 𝑚𝐹𝐸𝐻=(2𝑦). Find the values of 𝑥 and 𝑦.

  • A 𝑥 = 3 1 , 𝑦 = 3 4
  • B 𝑥 = 1 3 , 𝑦 = 1 0 0
  • C 𝑥 = 1 3 , 𝑦 = 2 9
  • D 𝑥 = 3 1 , 𝑦 = 1 0 0
  • E 𝑥 = 1 3 , 𝑦 = 1 0

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 𝑚𝐷.

Q14:

In the figure, 𝐴𝐵𝐶𝐷 and 𝐶𝐵𝐻𝑂 are parallelograms. Find 𝑚𝐴𝐵𝐻.

Q15:

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

Q16:

𝐴 𝐵 𝐶 𝐷 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 )
  • B 9 2 , 2
  • C ( 2 , 1 2 )
  • D ( 3 , 2 )

Q17:

In the figure shown, 𝑚𝐷𝐴𝐶=5𝑥, 𝑚𝐵𝐴𝐶=3𝑥, and 𝑚𝐴𝐵𝐶=4𝑥. Determine 𝑚𝐵𝐶𝐷 and 𝑚𝐴𝐷𝐶.

  • A 6 0 , 1 2 0
  • B 1 1 5 , 6 5
  • C 1 2 0 , 6 0
  • D 6 0 , 3 0

Q18:

Find 𝑚𝐶𝐵𝐷.

Q19:

In parallelogram 𝐴𝐵𝐶𝐷, suppose 𝑚𝐴+𝑚𝐶=222. What is 𝑚𝐵?

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?

  • A 𝐴 𝑋 + 𝐴 𝐵 = 𝐶 𝑌 + 𝐶 𝐷
  • B 𝐴 𝑋 + 𝐴 𝐵 > 𝐶 𝑌 + 𝐶 𝐷
  • C 𝐴 𝑋 + 𝐴 𝐵 < 𝐶 𝑌 + 𝐶 𝐷

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:

Is the following statement 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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