Lesson Worksheet: Parallel Lines in a Triangle Mathematics • 11th Grade

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In this worksheet, we will practice finding missing lengths in a triangle containing two or three parallel lines using proportionality.

Q1:

Using the diagram, which of the following is equal to 𝐴𝐵𝐴𝐷?

  • A𝐴𝐶𝐴𝐸
  • B𝐴𝐸𝐸𝐶
  • C𝐴𝐶𝐸𝐶
  • D𝐴𝐵𝐷𝐵
  • E𝐴𝐷𝐷𝐵

Q2:

Find the value of 𝑥.

Q3:

In the figure, 𝑋𝑌 and 𝐵𝐶 are parallel. If 𝐴𝑋=18, 𝑋𝐵=24, and 𝐴𝑌=27, what is the length of 𝑌𝐶?

Q4:

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

Q5:

Given that 𝐴𝐵𝐶𝐷 is a parallelogram, find the length of 𝑌𝑍.

Q6:

Find the length of 𝐶𝐵.

Q7:

If 𝐶𝐸=(𝑥+2)cm, what is 𝑥?

Q8:

If 𝐵𝑋=22cm, 𝐴𝑌=30cm, and 𝐴𝑋+𝐴𝑌𝐴𝐵+𝐴𝐶=1021, find the length of 𝐶𝑌.

Q9:

The given figure shows a triangle 𝐴𝐵𝐶.

Work out the value of 𝑥.

Work out the value of 𝑦.

Q10:

In the figure, 𝐴𝐷=10, 𝐴𝐸=5, 𝐵𝐷=4𝑥+2, and 𝐸𝐶=𝑥+3. What are the lengths of 𝐴𝐵 and 𝐸𝐶?

  • A𝐴𝐵=6, 𝐸𝐶=9
  • B𝐴𝐵=16, 𝐸𝐶=4
  • C𝐴𝐵=20, 𝐸𝐶=10
  • D𝐴𝐵=10, 𝐸𝐶=5
  • E𝐴𝐵=20, 𝐸𝐶=5

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