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

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.


Using the information in the figure, determine the length of 𝐸𝐹.


In the figure, lines 𝐿,𝐿,𝐿 , and 𝐿οŠͺ are all parallel. Given that 𝑋𝑍=12, 𝑍𝑁=8, 𝐴𝐡=10, and 𝐡𝐢=5, what is the length of 𝐢𝐷?


Find the lengths of 𝐸𝐢 and 𝐷𝐡.

  • A𝐸𝐢=21cm, 𝐷𝐡=16cm
  • B𝐸𝐢=28cm, 𝐷𝐡=21cm
  • C𝐸𝐢=14cm, 𝐷𝐡=24cm
  • D𝐸𝐢=16cm, 𝐷𝐡=24cm


Given that 𝐴𝐢=7.5cm, 𝐡𝐷=14cm, πΉπ‘Œ=25.2cm, and 𝐹𝐾=42cm, determine the lengths of 𝐢𝑋 and 𝐷𝐹.

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


In triangle 𝐴𝐡𝐢, 𝐴𝐸=1cm, 𝐸𝐢=2cm, and 𝐴𝐡=6cm. Find the length of 𝐴𝐹.


In the diagram below, 𝐴𝐡=10, 𝐡𝐢=(π‘₯+1), 𝐢𝐷=20, 𝐸𝐹=10, and 𝐹𝐺=10. Find the value of π‘₯ and the length of 𝐺𝐻.

  • Aπ‘₯=10, 𝐺𝐻=10
  • Bπ‘₯=10, 𝐺𝐻=20
  • Cπ‘₯=9, 𝐺𝐻=20
  • Dπ‘₯=9, 𝐺𝐻=5


Given that 𝐴𝐡=(2π‘₯+1)cm, 𝐡𝐢=(π‘₯+3)cm, 𝐷𝐸=(3π‘₯βˆ’1)cm, 𝐸𝐹=𝑦cm, 𝐺𝐻=11cm, and 𝐻𝐼=10cm, find the values of π‘₯ and 𝑦.

  • Aπ‘₯=7.27, 𝑦=5.09
  • Bπ‘₯=5.05, 𝑦=5.51
  • Cπ‘₯=2.56, 𝑦=6.06
  • Dπ‘₯=6.11, 𝑦=6.06


In the figure, 𝐴𝐡=3π‘₯, 𝐡𝐢=5π‘₯, 𝐷𝐸=(3π‘₯βˆ’6), and 𝐸𝐹=(4π‘₯βˆ’3). Find the value of π‘₯.


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


In the following figure, 𝐴𝐡=(5π‘₯+4)cm, 𝐡𝐢=(6π‘₯βˆ’4)cm, 𝐷𝐸=(4π‘₯βˆ’3)cm, and 𝐸𝐹=(4π‘¦βˆ’7)cm. Find the values of π‘₯ and 𝑦.

  • Aπ‘₯=8, 𝑦=5
  • Bπ‘₯=0, 𝑦=5
  • Cπ‘₯=8, 𝑦=9
  • Dπ‘₯=0, 𝑦=8

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