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

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 𝐴𝐡𝐴𝐷?

  • A𝐴𝐢𝐴𝐸
  • B𝐴𝐸𝐸𝐢
  • C𝐴𝐢𝐸𝐢
  • D𝐴𝐡𝐷𝐡
  • E𝐴𝐷𝐷𝐡

Q2:

Find the value of π‘₯.

Q3:

In the figure, π‘‹π‘Œ and 𝐡𝐢 are parallel. If 𝐴𝑋=18, 𝑋𝐡=24, and π΄π‘Œ=27, what is the length of π‘ŒπΆ?

Q4:

Given that 𝐴𝐡=24cm, 𝐴𝐷=36cm, 𝐴𝐢=18cm, and πΈπ‘Œ=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 𝐴𝐡𝐢𝐷 is a parallelogram, find the length of π‘Œπ‘.

Q6:

Find the length of 𝐢𝐡.

Q7:

If 𝐢𝐸=(π‘₯+2)cm, what is π‘₯?

Q8:

If 𝐡𝑋=22cm, π΄π‘Œ=30cm, and 𝐴𝑋+π΄π‘Œπ΄π΅+𝐴𝐢=1021, find the length of πΆπ‘Œ.

Q9:

The given figure shows a triangle 𝐴𝐡𝐢.

Work out the value of π‘₯.

Work out the value of 𝑦.

Q10:

In the figure, 𝐴𝐷=10, 𝐴𝐸=5, 𝐡𝐷=4π‘₯+2, and 𝐸𝐢=π‘₯+3. What are the lengths of 𝐴𝐡 and 𝐸𝐢?

  • A𝐴𝐡=6, 𝐸𝐢=9
  • B𝐴𝐡=16, 𝐸𝐢=4
  • C𝐴𝐡=20, 𝐸𝐢=10
  • D𝐴𝐡=10, 𝐸𝐢=5
  • E𝐴𝐡=20, 𝐸𝐢=5

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