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Lesson: Properties of Parallelograms

In this lesson, we will learn how to use the properties of parallelograms to solve problems.

Sample Question Videos

02:31
03:08

Worksheet • 25 Questions • 2 Videos

Q1:

In the figure below, given that 𝐴 𝐡 𝐢 𝐷 is a parallelogram, determine π‘š ∠ 𝐻 𝐷 𝐢 .

Q2:

In the figure below, given that 𝐴 𝐡 𝐢 𝐷 is a parallelogram, determine π‘š ∠ 𝐻 𝐷 𝐢 .

Q3:

In the parallelogram 𝐸 𝐹 𝐺 𝐻 , π‘š ∠ 𝐸 𝐻 𝐺 = ( 3 π‘₯ + 1 9 ) ∘ , π‘š ∠ 𝐻 𝐺 𝐹 = ( 2 π‘₯ + 6 ) ∘ , and π‘š ∠ 𝐹 𝐸 𝐻 = ( 2 𝑦 ) ∘ . Find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 3 1 , 𝑦 = 3 4
  • B π‘₯ = 1 3 , 𝑦 = 2 9
  • C π‘₯ = 1 3 , 𝑦 = 1 0 0
  • D π‘₯ = 1 3 , 𝑦 = 1 0
  • E π‘₯ = 3 1 , 𝑦 = 1 0 0

Q4:

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

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

Q5:

How many altitudes are there in a parallelogram?

Q6:

In the figure shown, π‘š ∠ 𝐷 𝐴 𝐢 = 5 π‘₯ ∘ , π‘š ∠ 𝐡 𝐴 𝐢 = 3 π‘₯ ∘ , and π‘š ∠ 𝐴 𝐡 𝐢 = 4 π‘₯ ∘ . Determine π‘š ∠ 𝐡 𝐢 𝐷 and π‘š ∠ 𝐴 𝐷 𝐢 .

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

Q7:

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

  • A base: 𝑂 𝐷 , altitude: 𝐸 𝐻
  • B base: 𝑂 𝐷 , altitude: 𝐷 𝑀
  • C base: 𝑂 𝐷 , altitude: 𝑂 π‘Œ
  • D base: 𝑂 π‘Œ , altitude: 𝐸 𝐻

Q8:

In the figure below, given that 𝐴 𝐡 𝐢 𝐷 is a parallelogram, find π‘š ∠ 𝐴 .

Q9:

𝐴 𝐡 𝐢 𝐷 is a parallelogram such that 𝐴 ( βˆ’ 3 , 4 ) , 𝐡 ( 0 , 4 ) , and 𝐢 ( βˆ’ 2 , 2 ) . Determine the coordinates of vertex 𝐷 .

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

Q10:

Find π‘š ∠ 𝐢 𝐡 𝐷 .

Q11:

Which of the following statements is not true?

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

Q12:

Find π‘š ∠ 𝐷 .

Q13:

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

Q14:

Find the lengths of 𝐢 𝐷 and 𝐷 𝐴 .

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

Q15:

In the figure, 𝐴 𝐡 𝐢 𝐷 and 𝐢 𝐡 𝐻 𝑂 are parallelograms. Find π‘š ∠ 𝐴 𝐡 𝐻 .

Q16:

In parallelogram 𝐴 𝐡 𝐢 𝐷 , suppose 𝐷 𝑋 = 4 4 and 𝐡 π‘Œ = 5 3 . How are the lengths 𝐴 𝑋 + 𝐴 𝐡 and 𝐢 π‘Œ + 𝐢 𝐷 related?

  • A 𝐴 𝑋 + 𝐴 𝐡 < 𝐢 π‘Œ + 𝐢 𝐷
  • B 𝐴 𝑋 + 𝐴 𝐡 > 𝐢 π‘Œ + 𝐢 𝐷
  • C 𝐴 𝑋 + 𝐴 𝐡 = 𝐢 π‘Œ + 𝐢 𝐷

Q17:

Given that 𝐴 𝐡 𝐢 𝐷 is a parallelogram, find the area of triangle 𝐴 𝐡 𝑀 .

Q18:

In parallelogram 𝐴 𝐡 𝐢 𝐷 , suppose π‘š ∠ 𝐴 + π‘š ∠ 𝐢 = 2 2 2 ∘ . What is π‘š ∠ 𝐡 ?

Q19:

Determine whether this statement is true or false: All parallelograms are regular polygons.

  • Atrue
  • Bfalse

Q20:

In the following figure is a parallelogram. What is the size of ?

  • A
  • B
  • C
  • D
  • E

Q21:

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

  • Afalse
  • Btrue

Q22:

𝐴 𝐡 𝐢 𝐷 is a parallelogram, where the coordinates of the points 𝐴 , 𝐡 , and 𝐢 are ( 4 , βˆ’ 9 ) , ( 3 , 2 ) , and ( 5 , 5 ) , respectively. Find the coordinates of the vertex 𝐷 .

  • A ( 6 , βˆ’ 6 )
  • B ο€Ό 9 2 , βˆ’ 2 
  • C ( 2 , βˆ’ 1 2 )
  • D ( 3 , βˆ’ 2 )

Q23:

Given that 𝐴 𝐡 𝐢 𝐷 is a parallelogram, find π‘₯ .

Q24:

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

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

Q25:

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