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Worksheet: Applications of Parallel Lines

In this worksheet, we will practice using parallelism of lines to find a missing length of a line segment in a transversal line cut by parallel lines.

Q1:

In the given figure, find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 2 , 𝑦 = 9
  • B π‘₯ = 1 2 , 𝑦 = 1 8
  • C π‘₯ = 6 , 𝑦 = 3 . 6
  • D π‘₯ = 6 , 𝑦 = 9
  • E π‘₯ = 3 , 𝑦 = 6

Q2:

In the given figure, find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 8 , 𝑦 = 1 . 5
  • B π‘₯ = 1 6 , 𝑦 = 9
  • C π‘₯ = 4 , 𝑦 = 1 . 8
  • D π‘₯ = 8 , 𝑦 = 9

Q3:

Find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 6 , 𝑦 = 2 1
  • B π‘₯ = 5 , 𝑦 = 2 5
  • C π‘₯ = 6 , 𝑦 = 2 9
  • D π‘₯ = 5 , 𝑦 = 1 7

Q4:

Find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 8 , 𝑦 = 2 1
  • B π‘₯ = 4 , 𝑦 = 9
  • C π‘₯ = 8 , 𝑦 = 1 7
  • D π‘₯ = 4 , 𝑦 = 1 3

Q5:

If 𝐢 𝐸 = ( π‘₯ + 2 ) c m , what is π‘₯ ?

Q6:

In the diagram below, 𝐴 𝐡 = 1 0 , 𝐡 𝐢 = ( π‘₯ + 1 ) , 𝐢 𝐷 = 2 0 , 𝐸 𝐹 = 1 0 , and 𝐹 𝐺 = 1 0 . Find the value of π‘₯ and the length of 𝐺 𝐻 .

  • A π‘₯ = 9 , 𝐺 𝐻 = 5
  • B π‘₯ = 1 0 , 𝐺 𝐻 = 2 0
  • C π‘₯ = 1 0 , 𝐺 𝐻 = 1 0
  • D π‘₯ = 9 , 𝐺 𝐻 = 2 0

Q7:

In the figure, 𝐴 𝐡 = 3 π‘₯ , 𝐡 𝐢 = 5 π‘₯ , 𝐷 𝐸 = ( 3 π‘₯ βˆ’ 6 ) , and 𝐸 𝐹 = ( 4 π‘₯ βˆ’ 3 ) . Find the value of π‘₯ .

Q8:

In the figure, 𝐴 𝐡 = 4 π‘₯ , 𝐡 𝐢 = 4 π‘₯ , 𝐷 𝐸 = ( 6 π‘₯ βˆ’ 5 ) , and 𝐸 𝐹 = ( 5 π‘₯ βˆ’ 3 ) . Find the value of π‘₯ .

Q9:

Using the information in the figure, determine the length of 𝐸 𝐹 .

Q10:

Given that 𝐴 𝐡 = 2 4 c m , 𝐴 𝐷 = 3 6 c m , 𝐴 𝐢 = 1 8 c m , and 𝐸 π‘Œ = 1 5 c m , find the length of 𝐴 𝐸 and 𝐷 𝑋 .

  • A 𝐴 𝐸 = 4 8 c m , 𝐷 𝑋 = 2 0 c m
  • B 𝐴 𝐸 = 2 1 c m , 𝐷 𝑋 = 1 6 c m
  • C 𝐴 𝐸 = 1 8 c m , 𝐷 𝑋 = 1 6 c m
  • D 𝐴 𝐸 = 2 7 c m , 𝐷 𝑋 = 2 0 c m

Q11:

Given the following figure, find the numerical values of π‘₯ and 𝑦 .

  • A π‘₯ = 7 3 , 𝑦 = 1 3
  • B π‘₯ = 8 , 𝑦 = 6 7
  • C π‘₯ = 7 3 , 𝑦 = 6 7
  • D π‘₯ = 8 , 𝑦 = 1 3

Q12:

Given the following figure, find the numerical values of π‘₯ and 𝑦 .

  • A π‘₯ = 5 2 , 𝑦 = 1 5
  • B π‘₯ = 9 , 𝑦 = 5 7
  • C π‘₯ = 5 2 , 𝑦 = 5 7
  • D π‘₯ = 9 , 𝑦 = 1 5

Q13:

In the figure, given that 𝐡 𝐢 = 9 4 , what is 𝐡 𝐸 ?

Q14:

Find the lengths of 𝐸 𝐢 and 𝐷 𝐡 .

  • A 𝐸 𝐢 = 2 8 c m , 𝐷 𝐡 = 2 1 c m
  • B 𝐸 𝐢 = 1 4 c m , 𝐷 𝐡 = 2 4 c m
  • C 𝐸 𝐢 = 1 6 c m , 𝐷 𝐡 = 2 4 c m
  • D 𝐸 𝐢 = 2 1 c m , 𝐷 𝐡 = 1 6 c m

Q15:

Given that 𝐴 𝐡 = ( 2 π‘₯ + 1 ) cm, 𝐡 𝐢 = ( π‘₯ + 3 ) cm, 𝐷 𝐸 = ( 3 π‘₯ βˆ’ 1 ) cm, 𝐸 𝐹 = 𝑦 c m , 𝐺 𝐻 = 1 1 c m , and 𝐻 𝐼 = 1 0 c m , find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 5 . 0 5 , 𝑦 = 5 . 5 1
  • B π‘₯ = 6 . 1 1 , 𝑦 = 6 . 0 6
  • C π‘₯ = 7 . 2 7 , 𝑦 = 5 . 0 9
  • D π‘₯ = 2 . 5 6 , 𝑦 = 6 . 0 6

Q16:

Given that 𝐴 𝐡 = ( 2 π‘₯ + 4 ) cm, 𝐷 𝐺 = ( 3 π‘₯ + 2 ) cm, 𝐴 𝐢 = ( 2 𝑦 + 2 ) cm, 𝐴 𝐺 = 4 c m , and 𝐴 𝐹 = 5 c m , find the lengths of 𝐴 𝐸 and 𝐷 𝐺 .

  • A 𝐴 𝐸 = 9 c m , 𝐷 𝐺 = 8 c m
  • B 𝐴 𝐸 = 2 c m , 𝐷 𝐺 = 4 c m
  • C 𝐴 𝐸 = 1 0 c m , 𝐷 𝐺 = 4 c m
  • D 𝐴 𝐸 = 1 5 c m , 𝐷 𝐺 = 8 c m

Q17:

In the following figure, 𝐴 𝐡 = ( 5 π‘₯ + 4 ) c m , 𝐡 𝐢 = ( 6 π‘₯ βˆ’ 4 ) c m , 𝐷 𝐸 = ( 4 π‘₯ βˆ’ 3 ) c m , and 𝐸 𝐹 = ( 4 𝑦 βˆ’ 7 ) c m . Find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 0 , 𝑦 = 8
  • B π‘₯ = 8 , 𝑦 = 5
  • C π‘₯ = 0 , 𝑦 = 5
  • D π‘₯ = 8 , 𝑦 = 9

Q18:

In the following figure, 𝐴 𝐡 = ( 7 π‘₯ + 4 ) c m , 𝐡 𝐢 = ( 6 π‘₯ + 5 ) c m , 𝐷 𝐸 = ( 5 π‘₯ + 5 ) c m , and 𝐸 𝐹 = ( 5 𝑦 + 5 ) c m . Find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 9 , 𝑦 = 5 0
  • B π‘₯ = 1 , 𝑦 = 3
  • C π‘₯ = 9 , 𝑦 = 3
  • D π‘₯ = 1 , 𝑦 = 1

Q19:

In the figure, lines 𝐿 , 𝐿 , 𝐿    , and 𝐿 οŠͺ are all parallel. Given that 𝑋 𝑍 = 1 2 , 𝑍 𝑁 = 8 , 𝐴 𝐡 = 1 0 , and 𝐡 𝐢 = 5 , what is the length of 𝐢 𝐷 ?

Q20:

Given that , , and , determine the values of and .

  • A ,
  • B ,
  • C ,
  • D ,

Q21:

Given that , , and , determine the values of and .

  • A ,
  • B ,
  • C ,
  • D ,

Q22:

Given that 𝐴 𝐢 = 7 . 5 c m , 𝐡 𝐷 = 1 4 c m , 𝐹 π‘Œ = 2 5 . 2 c m , and 𝐹 𝐾 = 4 2 c m , determine the lengths of 𝐢 𝑋 and 𝐷 𝐹 .

  • A 36 cm, 22.5 cm
  • B 37.5 cm, 42 cm
  • C 67.2 cm, 22.5 cm
  • D 36 cm, 42 cm

Q23:

Given that 𝐴 𝐢 = 1 0 . 5 c m , 𝐡 𝐷 = 1 8 . 5 c m , 𝐹 π‘Œ = 3 3 . 3 c m , and 𝐹 𝐾 = 5 5 . 5 c m , determine the lengths of 𝐢 𝑋 and 𝐷 𝐹 .

  • A 50.4 cm, 31.5 cm
  • B 52.5 cm, 55.5 cm
  • C 88.8 cm, 31.5 cm
  • D 50.4 cm, 55.5 cm

Q24:

Given that 𝐴 𝐷 = π‘₯ c m , 𝐷 𝐡 = 3 0 c m , 𝐡 𝐸 = ( π‘₯ + 7 ) c m , and 𝐸 𝐢 = 1 8 c m , find the value of π‘₯ .

Q25:

Given that 𝐴 𝐷 = π‘₯ c m , 𝐷 𝐡 = 4 5 c m , 𝐡 𝐸 = ( π‘₯ + 3 ) c m , and 𝐸 𝐢 = 2 2 c m , find the value of π‘₯ .

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