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 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:

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, 𝑚∠𝐸𝐻𝐺=(3𝑥+19)∘, 𝑚∠𝐻𝐺𝐹=(2𝑥+6)∘, and 𝑚∠𝐹𝐸𝐻=(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 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:

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

  • 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 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?

  • 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

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.