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

Start Practising

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 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

This lesson includes 22 additional questions and 171 additional question variations for subscribers.

GET YOUR PORTAL NOW

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.