Lesson Worksheet: Parallel Lines and Transversals: Proportional Parts Mathematics • 11th Grade

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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:

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?

Q3:

Find the lengths of 𝐸𝐶 and 𝐷𝐵.

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

Q4:

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

Q5:

In triangle 𝐴𝐵𝐶, 𝐴𝐸=1cm, 𝐸𝐶=2cm, and 𝐴𝐵=6cm. Find the length of 𝐴𝐹.

Q6:

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

Q7:

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

Q8:

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

Q9:

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

Q10:

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

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