Worksheet: Parallel Lines and Transversals: 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 𝐸𝐹.

Q2:

Given that 𝐴𝐶=7.5cm, 𝐵𝐷=14cm, 𝐹𝑌=25.2cm, and 𝐹𝐾=42cm, determine the lengths of 𝐶𝑋 and 𝐷𝐹.

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

Q3:

If 𝐶𝐸=(𝑥+2)cm, what is 𝑥?

Q4:

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

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

Q5:

Given that 𝐴𝐷=𝑥cm, 𝐷𝐵=30cm, 𝐵𝐸=(𝑥+7)cm, and 𝐸𝐶=18cm, find the value of 𝑥.

Q6:

In the figure, lines 𝐿,𝐿,𝐿 , and 𝐿 are all parallel. Given that 𝑋𝑍=12, 𝑍𝑁=8, 𝐴𝐵=10, and 𝐵𝐶=5, what is the length of 𝐶𝐷?

Q7:

Find the lengths of 𝐸𝐶 and 𝐷𝐵.

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

Q8:

Given that 𝐴𝐵=24cm, 𝐴𝐷=36cm, 𝐴𝐶=18cm, and 𝐸𝑌=15cm, find the length of 𝐴𝐸 and 𝐷𝑋.

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

Q9:

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

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

Q10:

In the figure, 𝐴𝐵=3𝑥, 𝐵𝐶=5𝑥, 𝐷𝐸=(3𝑥−6), and 𝐸𝐹=(4𝑥−3). Find the value of 𝑥.

Q11:

In the following figure, 𝐴𝐵=(5𝑥+4)cm, 𝐵𝐶=(6𝑥−4)cm, 𝐷𝐸=(4𝑥−3)cm, and 𝐸𝐹=(4𝑦−7)cm. Find the values of 𝑥 and 𝑦.

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

Q12:

Given that 𝐴𝐵=(2𝑥+4) cm, 𝐷𝐺=(3𝑥+2) cm, 𝐴𝐶=(2𝑦+2) cm, 𝐴𝐺=4cm, and 𝐴𝐹=5cm, find the lengths of 𝐴𝐸 and 𝐷𝐺.

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

Q13:

Find the values of 𝑥 and 𝑦.

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

Q14:

Given that 𝐴𝐵=(2𝑥+1)cm, 𝐵𝐶=(𝑥+3)cm, 𝐷𝐸=(3𝑥−1)cm, 𝐸𝐹=𝑦cm, 𝐺𝐻=11cm, and 𝐻𝐼=10cm, find the values of 𝑥 and 𝑦.

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

Q15:

Given that 𝑀𝐶=15cm, 𝑀𝐷=10cm, and 𝐴𝑀=𝐷𝐹, determine the values of 𝑥 and 𝑦.

  • A 𝑥 = 8 , 𝑦 = 3
  • B 𝑥 = 4 , 𝑦 = 4
  • C 𝑥 = 6 , 𝑦 = 2 8
  • D 𝑥 = 8 , 𝑦 = 2 8

Q16:

In the diagram below, 𝐴𝐵=10, 𝐵𝐶=(𝑥+1), 𝐶𝐷=20, 𝐸𝐹=10, and 𝐹𝐺=10. Find the value of 𝑥 and the length of 𝐺𝐻.

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

Q17:

In the figure, given that 𝐵𝐶=94, what is 𝐵𝐸?

Q18:

Suppose 𝑋𝑌 and 𝑍𝐿 intersect at point 𝑀, and that 𝑋𝑍 and 𝐿𝑌 are parallel. If 𝑋𝑀=46, 𝑌𝑀=64, and 𝑍𝐿=165, what is 𝑍𝑀?

Q19:

Suppose that, in the figure, 𝐴𝐶=30 and 𝑚∠𝐸𝐷𝐵=139∘. What is the length of 𝐴𝐸?

Q20:

Given that 𝑋𝐿=9cm, find the length of 𝑋𝑍.

Q21:

Given that 𝐸𝐷∥𝐶𝐵, find the value of 𝑥.

Q22:

Draw △𝐴𝐵𝐶 with 𝐴𝐵=8, 𝑚∠𝐴=39∘, and 𝑚∠𝐵=68∘. Bisect 𝐴𝐶 at 𝐷, and draw ⃖⃗𝐷𝐸 parallel to 𝐴𝐵 and meeting 𝐵𝐶 at 𝐸. Find the lengths 𝐵𝐸, 𝐶𝐸, and 𝐷𝐸 rounded to one decimal place.

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

Q23:

Given that 𝐴𝑌=16cm, 𝐷𝑌=21cm, and 𝐴𝐵=88.53cm, find the perimeter of △𝐴𝐷𝑌. 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 𝐴𝐵𝐵𝐶=23, 𝐴𝐷=15cm, and 𝐶𝐹=13cm, find the length of 𝐵𝐸.

Q25:

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

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

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