Worksheet: Parallel Lines and Proportional Parts

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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:

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

Q2:

Given that 𝐴 𝐶 = 7 . 5 c m , 𝐵 𝐷 = 1 4 c m , 𝐹 𝑌 = 2 5 . 2 c m , and 𝐹 𝐾 = 4 2 c m , determine the lengths of 𝐶 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

Q3:

If 𝐶 𝐸 = ( 𝑥 + 2 ) c m , what is 𝑥 ?

Q4:

In the given figure, find the values of 𝑥 and 𝑦 .

  • A 𝑥 = 2 , 𝑦 = 9
  • B 𝑥 = 1 2 , 𝑦 = 1 8
  • C 𝑥 = 6 , 𝑦 = 3 . 6
  • D 𝑥 = 6 , 𝑦 = 9
  • E 𝑥 = 3 , 𝑦 = 6

Q5:

Given that 𝐴 𝐷 = 𝑥 c m , 𝐷 𝐵 = 3 0 c m , 𝐵 𝐸 = ( 𝑥 + 7 ) c m , and 𝐸 𝐶 = 1 8 c m , find the value of 𝑥 .

Q6:

In the figure, lines 𝐿 , 𝐿 , 𝐿 , and 𝐿 are all parallel. Given that 𝑋 𝑍 = 1 2 , 𝑍 𝑁 = 8 , 𝐴 𝐵 = 1 0 , and 𝐵 𝐶 = 5 , what is the length of 𝐶 𝐷 ?

Q7:

Find the lengths of 𝐸 𝐶 and 𝐷 𝐵 .

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

Q8:

Given that 𝐴 𝐵 = 2 4 c m , 𝐴 𝐷 = 3 6 c m , 𝐴 𝐶 = 1 8 c m , and 𝐸 𝑌 = 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

Q9:

Given the following figure, find the numerical values of 𝑥 and 𝑦 .

  • A 𝑥 = 7 3 , 𝑦 = 1 3
  • B 𝑥 = 8 , 𝑦 = 6 7
  • C 𝑥 = 7 3 , 𝑦 = 6 7
  • D 𝑥 = 8 , 𝑦 = 1 3

Q10:

In the figure, 𝐴 𝐵 = 3 𝑥 , 𝐵 𝐶 = 5 𝑥 , 𝐷 𝐸 = ( 3 𝑥 − 6 ) , and 𝐸 𝐹 = ( 4 𝑥 − 3 ) . Find the value of 𝑥 .

Q11:

In the following figure, 𝐴 𝐵 = ( 5 𝑥 + 4 ) c m , 𝐵 𝐶 = ( 6 𝑥 − 4 ) c m , 𝐷 𝐸 = ( 4 𝑥 − 3 ) c m , and 𝐸 𝐹 = ( 4 𝑦 − 7 ) c m . Find the values of 𝑥 and 𝑦 .

  • A 𝑥 = 0 , 𝑦 = 8
  • B 𝑥 = 8 , 𝑦 = 5
  • C 𝑥 = 0 , 𝑦 = 5
  • D 𝑥 = 8 , 𝑦 = 9

Q12:

Given that 𝐴 𝐵 = ( 2 𝑥 + 4 ) cm, 𝐷 𝐺 = ( 3 𝑥 + 2 ) cm, 𝐴 𝐶 = ( 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

Q13:

Find the values of 𝑥 and 𝑦 .

  • A 𝑥 = 6 , 𝑦 = 2 1
  • B 𝑥 = 5 , 𝑦 = 2 5
  • C 𝑥 = 6 , 𝑦 = 2 9
  • D 𝑥 = 5 , 𝑦 = 1 7

Q14:

Given that 𝐴 𝐵 = ( 2 𝑥 + 1 ) cm, 𝐵 𝐶 = ( 𝑥 + 3 ) cm, 𝐷 𝐸 = ( 3 𝑥 − 1 ) cm, 𝐸 𝐹 = 𝑦 c m , 𝐺 𝐻 = 1 1 c m , and 𝐻 𝐼 = 1 0 c m , find the values of 𝑥 and 𝑦 .

  • A 𝑥 = 5 . 0 5 , 𝑦 = 5 . 5 1
  • B 𝑥 = 6 . 1 1 , 𝑦 = 6 . 0 6
  • C 𝑥 = 7 . 2 7 , 𝑦 = 5 . 0 9
  • D 𝑥 = 2 . 5 6 , 𝑦 = 6 . 0 6

Q15:

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

  • A ,
  • B ,
  • C ,
  • D ,

Q16:

In the diagram below, 𝐴 𝐵 = 1 0 , 𝐵 𝐶 = ( 𝑥 + 1 ) , 𝐶 𝐷 = 2 0 , 𝐸 𝐹 = 1 0 , and 𝐹 𝐺 = 1 0 . Find the value of 𝑥 and the length of 𝐺 𝐻 .

  • A 𝑥 = 9 , 𝐺 𝐻 = 5
  • B 𝑥 = 1 0 , 𝐺 𝐻 = 2 0
  • C 𝑥 = 1 0 , 𝐺 𝐻 = 1 0
  • D 𝑥 = 9 , 𝐺 𝐻 = 2 0

Q17:

In the figure, given that 𝐵 𝐶 = 9 4 , what is 𝐵 𝐸 ?

Q18:

Suppose 𝑋 𝑌 and 𝑍 𝐿 intersect at point 𝑀 , and that 𝑋 𝑍 and 𝐿 𝑌 are parallel. If 𝑋 𝑀 = 4 6 , 𝑌 𝑀 = 6 4 , and 𝑍 𝐿 = 1 6 5 , what is 𝑍 𝑀 ?

Q19:

Suppose that, in the figure, 𝐴 𝐶 = 3 0 and 𝑚 ∠ 𝐸 𝐷 𝐵 = 1 3 9 ∘ . What is the length of 𝐴 𝐸 ?

Q20:

Given that 𝑋 𝐿 = 9 c m , find the length of 𝑋 𝑍 .

Q21:

Given that 𝐸 𝐷 ∥ 𝐶 𝐵 , find the value of 𝑥 .

Q22:

Draw △ 𝐴 𝐵 𝐶 with 𝐴 𝐵 = 8 , 𝑚 ∠ 𝐴 = 3 9 ∘ , and 𝑚 ∠ 𝐵 = 6 8 ∘ . Bisect 𝐴 𝐶 at 𝐷 , and draw ⃖ ⃗ 𝐷 𝐸 parallel to 𝐴 𝐵 and meeting 𝐵 𝐶 at 𝐸 . Find the lengths 𝐵 𝐸 , 𝐶 𝐸 , and 𝐷 𝐸 rounded to one decimal place.

  • A 𝐵 𝐸 ≈ 5 . 2 , 𝐶 𝐸 ≈ 5 . 2 , 𝐷 𝐸 ≈ 4 . 0
  • B 𝐵 𝐸 ≈ 4 . 0 , 𝐶 𝐸 ≈ 4 . 0 , 𝐷 𝐸 ≈ 2 . 6
  • C 𝐵 𝐸 ≈ 8 . 0 , 𝐶 𝐸 ≈ 8 . 0 , 𝐷 𝐸 ≈ 2 . 6
  • D 𝐵 𝐸 ≈ 2 . 6 , 𝐶 𝐸 ≈ 2 . 6 , 𝐷 𝐸 ≈ 4 . 0

Q23:

Given that 𝐴 𝑌 = 1 6 c m , 𝐷 𝑌 = 2 1 c m , and 𝐴 𝐵 = 8 8 . 5 3 c m , find the perimeter of △ 𝐴 𝐷 𝑌 . Round your answer to two decimal places.

Q24:

𝑋 , 𝑌 , and 𝑍 are three parallel planes intersected by the two coplanar straight lines 𝐿 and 𝐿 . If 𝐴 𝐵 𝐵 𝐶 = 2 3 , 𝐴 𝐷 = 1 5 c m , and 𝐶 𝐹 = 1 3 c m , find the length of 𝐵 𝐸 .

Q25:

In the given figure, find the values of 𝑥 and 𝑦 .

  • A 𝑥 = 8 , 𝑦 = 1 . 5
  • B 𝑥 = 1 6 , 𝑦 = 9
  • C 𝑥 = 4 , 𝑦 = 1 . 8
  • D 𝑥 = 8 , 𝑦 = 9

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