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Lesson: Diagonals of Parallelograms

Sample Question Videos

Worksheet • 18 Questions • 1 Video

Q1:

Find the value of 𝑧 in the following parallelogram.

Q2:

Find the value of 𝑧 in the following parallelogram.

Q3:

In parallelogram 𝐴 𝐡 𝐢 𝐷 , 𝐡 𝐢 = 8 9 , 𝑀 𝐡 = 4 6 , and 𝑀 𝐢 = 7 8 . What is the perimeter of β–³ 𝐴 𝑀 𝐷 ?

Q4:

In parallelogram 𝐴 𝐡 𝐢 𝐷 , 𝐡 𝐢 = 4 7 , 𝑀 𝐡 = 4 3 , and 𝑀 𝐢 = 3 3 . What is the perimeter of β–³ 𝐴 𝑀 𝐷 ?

Q5:

If 𝑄 𝑅 𝑆 𝑇 is a parallelogram, find the value of 𝑧 .

Q6:

If 𝑄 𝑅 𝑆 𝑇 is a parallelogram, find the value of 𝑧 .

Q7:

𝐴 𝐡 𝐢 𝐷 is a parallelogram where the coordinates of 𝐴 are ( 7 , 7 ) and the coordinates of 𝐢 are ( βˆ’ 1 , 5 ) . Find the coordinates of the point of intersection of the two diagonals of 𝐴 𝐡 𝐢 𝐷 .

  • A ( 3 , 6 )
  • B ( 7 , 7 )
  • C ( 4 , 6 )
  • D ( βˆ’ 1 , 5 )

Q8:

𝐴 𝐡 𝐢 𝐷 is a parallelogram where the coordinates of 𝐴 are ( 7 , 5 ) and the coordinates of 𝐢 are ( βˆ’ 1 , 3 ) . Find the coordinates of the point of intersection of the two diagonals of 𝐴 𝐡 𝐢 𝐷 .

  • A ( 3 , 4 )
  • B ( 7 , 5 )
  • C ( 4 , 4 )
  • D ( βˆ’ 1 , 3 )

Q9:

What can you say about the diagonals of a parallelogram?

  • AThey are perpendicular.
  • BThey bisect each other.
  • CThey are equal in length.

Q10:

In parallelogram 𝐴 𝐡 𝐢 𝐷 , the coordinates of 𝐴 are ( 1 , 3 ) and those of the intersection of the diagonals are ( 4 , βˆ’ 3 ) . What are the coordinates of point 𝐢 ?

  • A ( 7 , βˆ’ 9 )
  • B ( 3 , βˆ’ 6 )
  • C ο€Ό 5 2 , 0 
  • D ( βˆ’ 9 , 7 )
  • E ο€Ό 1 2 , 2 

Q11:

Given that 𝐴 𝐡 𝐢 𝐷 is a parallelogram and 𝐢 𝑀 = 8 . 6 c m , find the perimeter of β–³ 𝐴 𝐡 𝐢 .

Q12:

Given that 𝐴 𝐡 𝐢 𝐷 is a parallelogram and 𝐢 𝑀 = 5 . 8 c m , find the perimeter of β–³ 𝐴 𝐡 𝐢 .

Q13:

In a parallelogram 𝐴 𝐡 𝐢 𝐷 , the coordinates of 𝐴 , 𝐡 , and 𝐢 are ( 9 , 0 ) , ( 1 1 , 0 ) , and ( βˆ’ 4 , 9 ) , respectively. Find the coordinates of the point at which the two diagonals intersect, and then determine the coordinates of point 𝐷 .

  • A ο€Ό 5 2 , 9 2  , ( βˆ’ 6 , 9 )
  • B ( 5 , 9 ) , ( 6 , βˆ’ 9 )
  • C ( 1 3 , βˆ’ 9 ) , ( 6 , 9 )
  • D ο€Ό 1 3 2 , βˆ’ 9 2  , ( βˆ’ 6 , βˆ’ 9 )

Q14:

In a parallelogram 𝐴 𝐡 𝐢 𝐷 , the coordinates of 𝐴 , 𝐡 , and 𝐢 are ( βˆ’ 8 , 5 ) , ( 6 , 5 ) , and ( 1 3 , 8 ) , respectively. Find the coordinates of the point at which the two diagonals intersect, and then determine the coordinates of point 𝐷 .

  • A ο€Ό 5 2 , 1 3 2  , ( βˆ’ 1 , 8 )
  • B ( 5 , 1 3 ) , ( 1 , βˆ’ 8 )
  • C ( βˆ’ 2 1 , βˆ’ 3 ) , ( 1 , 8 )
  • D ο€Ό βˆ’ 2 1 2 , βˆ’ 3 2  , ( βˆ’ 1 , βˆ’ 8 )

Q15:

Given that 𝐢 𝑀 = 1 6 c m , determine the length of 𝐴 𝐢 .

Q16:

The given figure shows a parallelogram 𝐴 𝐡 𝐢 𝐷 .

Using what you know about alternate angles, determine which angle will have the same measure as ∠ 𝐴 𝐡 𝐷 .

  • A ∠ 𝐡 𝐷 𝐢
  • B ∠ 𝐢 𝐡 𝐴
  • C ∠ 𝐡 𝐢 𝐷
  • D ∠ 𝐡 𝐷 𝐴
  • E ∠ 𝐡 𝐴 𝐷

Which angle will be equal in measure to ∠ 𝐴 𝐷 𝐡 ?

  • A ∠ 𝐢 𝐡 𝐷
  • B ∠ 𝐴 𝐷 𝐢
  • C ∠ 𝐡 𝐷 𝐢
  • D ∠ 𝐢 𝐡 𝐴
  • E ∠ 𝐡 𝐴 𝐷

𝐡 𝐷 is a common side to both triangles. Using the information from the earlier parts of the question, can we prove that triangles 𝐴 𝐡 𝐷 and 𝐢 𝐷 𝐡 are congruent? If yes, by which congruence criteria?

  • AYes, by ASA
  • BNo
  • CYes, by SSS
  • DYes, by HL
  • EYes, by SAS

What will be true of 𝐴 𝐡 and 𝐢 𝐷 and of 𝐡 𝐢 and 𝐴 𝐷 ?

  • A 𝐴 𝐡 = 𝐢 𝐷 , 𝐴 𝐷 = 𝐡 𝐢
  • B 𝐴 𝐡 β‰  𝐢 𝐷 , 𝐴 𝐷 = 𝐡 𝐢
  • C 𝐴 𝐡 β‰  𝐢 𝐷 , 𝐴 𝐷 β‰  𝐡 𝐢
  • D 𝐴 𝐡 = 𝐢 𝐷 , 𝐴 𝐷 β‰  𝐡 𝐢

What will be true of angles ∠ 𝐡 𝐴 𝐷 and ∠ 𝐡 𝐢 𝐷 and of angles ∠ 𝐴 𝐡 𝐢 and ∠ 𝐴 𝐷 𝐢 ?

  • A π‘š ∠ 𝐡 𝐴 𝐷 = π‘š ∠ 𝐡 𝐢 𝐷 , π‘š ∠ 𝐴 𝐡 𝐢 = π‘š ∠ 𝐴 𝐷 𝐢
  • B π‘š ∠ 𝐡 𝐴 𝐷 β‰  π‘š ∠ 𝐡 𝐢 𝐷 , π‘š ∠ 𝐴 𝐡 𝐢 β‰  π‘š ∠ 𝐴 𝐷 𝐢
  • C π‘š ∠ 𝐡 𝐴 𝐷 = π‘š ∠ 𝐡 𝐢 𝐷 , π‘š ∠ 𝐴 𝐡 𝐢 β‰  π‘š ∠ 𝐴 𝐷 𝐢
  • D π‘š ∠ 𝐡 𝐴 𝐷 β‰  π‘š ∠ 𝐡 𝐢 𝐷 , π‘š ∠ 𝐴 𝐡 𝐢 = π‘š ∠ 𝐴 𝐷 𝐢

Q17:

Is any quadrilateral whose diagonals bisect each other a parallelogram?

  • Ano
  • Byes

Q18:

Are the two diagonals of a parallelogram perpendicular?

  • Ayes
  • Bno
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