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.

  • A36 cm, 22.5 cm
  • B36 cm, 42 cm
  • C67.2 cm, 22.5 cm
  • D37.5 cm, 42 cm

Q3:

If 𝐶𝐸=(𝑥+2)cm, what is 𝑥?

Q4:

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

  • A𝑥=3, 𝑦=6
  • B𝑥=6, 𝑦=3.6
  • C𝑥=12, 𝑦=18
  • D𝑥=6, 𝑦=9
  • E𝑥=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.

  • A𝐸𝐶=21cm, 𝐷𝐵=16cm
  • B𝐸𝐶=28cm, 𝐷𝐵=21cm
  • C𝐸𝐶=14cm, 𝐷𝐵=24cm
  • D𝐸𝐶=16cm, 𝐷𝐵=24cm

Q8:

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

  • A𝐴𝐸=21cm, 𝐷𝑋=16cm
  • B𝐴𝐸=48cm, 𝐷𝑋=20cm
  • C𝐴𝐸=27cm, 𝐷𝑋=20cm
  • D𝐴𝐸=18cm, 𝐷𝑋=16cm

Q9:

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

  • A𝑥=8, 𝑦=67
  • B𝑥=73, 𝑦=67
  • C𝑥=73, 𝑦=13
  • D𝑥=8, 𝑦=13

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.

  • A𝑥=8, 𝑦=5
  • B𝑥=0, 𝑦=5
  • C𝑥=8, 𝑦=9
  • D𝑥=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.

  • A𝐴𝐸=2cm, 𝐷𝐺=4cm
  • B𝐴𝐸=15cm, 𝐷𝐺=8cm
  • C𝐴𝐸=10cm, 𝐷𝐺=4cm
  • D𝐴𝐸=9cm, 𝐷𝐺=8cm

Q13:

Find the values of 𝑥 and 𝑦.

  • A𝑥=5, 𝑦=25
  • B𝑥=6, 𝑦=21
  • C𝑥=6, 𝑦=29
  • D𝑥=5, 𝑦=17

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.

  • A𝑥=7.27, 𝑦=5.09
  • B𝑥=5.05, 𝑦=5.51
  • C𝑥=2.56, 𝑦=6.06
  • D𝑥=6.11, 𝑦=6.06

Q15:

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

  • A𝑥=8, 𝑦=3
  • B𝑥=4, 𝑦=4
  • C𝑥=6, 𝑦=28
  • D𝑥=8, 𝑦=28

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.

  • A𝑥=10, 𝐺𝐻=10
  • B𝑥=10, 𝐺𝐻=20
  • C𝑥=9, 𝐺𝐻=20
  • D𝑥=9, 𝐺𝐻=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.

  • A𝐵𝐸≈8.0, 𝐶𝐸≈8.0, 𝐷𝐸≈2.6
  • B𝐵𝐸≈4.0, 𝐶𝐸≈4.0, 𝐷𝐸≈2.6
  • C𝐵𝐸≈5.2, 𝐶𝐸≈5.2, 𝐷𝐸≈4.0
  • D𝐵𝐸≈2.6, 𝐶𝐸≈2.6, 𝐷𝐸≈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.

  • A𝑥=4, 𝑦=1.8
  • B𝑥=8, 𝑦=1.5
  • C𝑥=16, 𝑦=9
  • D𝑥=8, 𝑦=9

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