Lesson Worksheet: Parallel Lines and Proportional Parts Mathematics

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In this worksheet, we will practice using parallel lines and proportional parts to solve problems.

Q1:

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

Q2:

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

Q3:

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

Q4:

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

Q5:

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

Q6:

True or False: In the given figure, 𝑎𝑏=𝑐𝑑.

  • ATrue
  • BFalse

Q7:

True or False: In the figure, 𝐹 is the midpoint of 𝐶𝐷.

  • ATrue
  • BFalse

Q8:

In the given triangle 𝐴𝐵𝐶, 𝐴𝐸=1cm, 𝐴𝐹=3cm, 𝐶𝐸=2cm, and 𝐹𝐵=𝑥−1cm. Find the value of 𝑥.

Q9:

Using the information in the figure, find the value of 𝑥.

Q10:

Use the figure to determine the values of 𝑥 and 𝑦.

  • A15, 10
  • B8, 1
  • C8, 3
  • D15, 3

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