Worksheet: Properties of Parallelograms

Practice

In this worksheet, we will practice using the properties of parallelograms to solve problems.

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.

  • Afalse
  • Btrue

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 contains 2 pairs of parallel sides.
  • EIt has 2 sets of perpendicular and parallel sides.

Q4:

Find the lengths of 𝐶 𝐷 and 𝐷 𝐴 .

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

Q5:

Given that 𝐴 𝐵 𝐶 𝐷 is a parallelogram and 𝑚 ∠ 𝐶 = 6 8 ∘ , find 𝑚 ∠ 𝐴 .

Q6:

In the figure below, given that 𝐴 𝐵 𝐶 𝐷 is a parallelogram, determine 𝑚 ∠ 𝐻 𝐷 𝐶 .

Q7:

In the figure below, given that 𝐴 𝐵 𝐶 𝐷 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 ( − 1 , 6 )
  • B ( 1 , 2 )
  • C ( − 6 , 1 )
  • D ( − 5 , 2 )
  • E ( − 7 , − 3 )

Q9:

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

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

Q10:

In the parallelogram 𝐸 𝐹 𝐺 𝐻 , 𝑚 ∠ 𝐸 𝐻 𝐺 = ( 3 𝑥 + 1 9 ) ∘ , 𝑚 ∠ 𝐻 𝐺 𝐹 = ( 2 𝑥 + 6 ) ∘ , and 𝑚 ∠ 𝐹 𝐸 𝐻 = ( 2 𝑦 ) ∘ . Find the values of 𝑥 and 𝑦 .

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

Q11:

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

Q12:

In the following figure 𝐴 𝐵 𝐶 𝐷 is a parallelogram. What is the measure of ∠ 𝐴 ?

Q13:

Find 𝑚 ∠ 𝐷 .

Q14:

In the figure, 𝐴 𝐵 𝐶 𝐷 and 𝐶 𝐵 𝐻 𝑂 are parallelograms. Find 𝑚 ∠ 𝐴 𝐵 𝐻 .

Q15:

Given that 𝐴 𝐵 𝐶 𝐷 is a parallelogram, find the area of triangle 𝐴 𝐵 𝑀 .

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 ( 3 , − 2 )
  • B 9 2 , − 2
  • C ( 2 , − 1 2 )
  • D ( 6 , − 6 )

Q17:

In the figure shown, 𝑚 ∠ 𝐷 𝐴 𝐶 = 5 𝑥 ∘ , 𝑚 ∠ 𝐵 𝐴 𝐶 = 3 𝑥 ∘ , and 𝑚 ∠ 𝐴 𝐵 𝐶 = 4 𝑥 ∘ . Determine 𝑚 ∠ 𝐵 𝐶 𝐷 and 𝑚 ∠ 𝐴 𝐷 𝐶 .

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

Q18:

Find 𝑚 ∠ 𝐶 𝐵 𝐷 .

Q19:

In parallelogram 𝐴 𝐵 𝐶 𝐷 , suppose 𝑚 ∠ 𝐴 + 𝑚 ∠ 𝐶 = 2 2 2 ∘ . What is 𝑚 ∠ 𝐵 ?

Q20:

Given that 𝐴 𝐵 𝐶 𝐷 is a parallelogram, find 𝑥 .

Q21:

In parallelogram 𝐴 𝐵 𝐶 𝐷 , suppose 𝐷 𝑋 = 4 4 and 𝐵 𝑌 = 5 3 . How are the lengths 𝐴 𝑋 + 𝐴 𝐵 and 𝐶 𝑌 + 𝐶 𝐷 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?

  • A base: 𝑂 𝑌 , altitude: 𝐸 𝐻
  • B base: 𝑂 𝐷 , altitude: 𝐷 𝑀
  • C base: 𝑂 𝐷 , altitude: 𝑂 𝑌
  • D base: 𝑂 𝐷 , altitude: 𝐸 𝐻

Q24:

Which of the following statements is not true?

  • A Squares have four congruent angles and sides.
  • B Opposite sides in a parallelogram are parallel.
  • C Rhombuses have four congruent sides.
  • D Parallelograms have exactly one pair of parallel sides.
  • E Rectangles 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.

  • Afalse
  • Btrue

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