Worksheet: Parallel Lines in a Triangle

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

Q1:

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

Q2:

Determine 𝐴𝐵𝐵𝐷, if 𝐴𝐷𝐷𝐵=3823.

  • A 3 8 6 1
  • B 6 1 3 8
  • C 6 1 2 3
  • D 2 3 6 1

Q3:

In the figure, 𝐷𝑋 and 𝐸𝑌 are parallel to 𝐴𝐶 and 𝐴𝐵 respectively. If 𝐵𝐶=12cm, 𝐴𝐷𝐷𝐵=2, and 𝐸𝐶=13𝐴𝐸, determine the length of 𝑋𝑌.

Q4:

Find the length of 𝐶𝐵.

Q5:

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

Q6:

If the perimeter of 𝐴𝐵𝐶=9.7cm, 𝐸 is the midpoint of 𝐴𝐶, and 𝐷𝐸𝐵𝐶, find the length of 𝐷𝐸.

Q7:

Given that 𝑍 is the midpoint of 𝐷𝐶, the perimeter of 𝐴𝐷𝐶 is 33 cm, 𝐴𝐷=7cm, and 𝑍𝐶=5cm, find the length of 𝐴𝑌.

Q8:

Given that 𝐴𝐸𝐹𝐷 is a parallelogram, where 𝐸 and 𝐹 are the midpoints of 𝐷𝐵 and 𝐷𝐶 respectively, find the length of 𝐶𝐵.

Q9:

Given that 𝐴𝐵𝐶𝐷 is a parallelogram, find 𝑚𝐵𝐴𝐸.

Q10:

On the figure, 𝐴𝐵𝐶𝐷 is a parallelogram whose diagonals intersect at 𝑀, and 𝑋 is a point on 𝐴𝐷. If 𝑀𝑋=38, what is 𝐶𝐷?

Q11:

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

Q12:

𝐹 𝐷 𝐸 𝐶 is a parallelogram, where 𝐹 and 𝐷 are the midpoints of 𝐴𝐵 and 𝐴𝐶, respectively, and 𝐶𝐸=6cm. Determine the length of 𝐵𝐶.

Q13:

Given that the area of the parallelogram 𝐴𝐵𝐶𝐷=1,743cm and that of the 𝐴𝐹𝐷=268cm, find the area of 𝐹𝐵𝐶𝐿 and that of the 𝐿𝐶𝐹.

  • A area of 𝐹𝐵𝐶𝐿=871.5cm, area of 𝐿𝐶𝐹=1,475cm
  • B area of 𝐹𝐵𝐶𝐿=1,475cm, area of 𝐿𝐶𝐹=871.5cm
  • C area of 𝐹𝐵𝐶𝐿=435.75cm, area of 𝐿𝐶𝐹=1,475cm
  • D area of 𝐹𝐵𝐶𝐿=1,475cm, area of 𝐿𝐶𝐹=435.75cm
  • E area of 𝐹𝐵𝐶𝐿=1,743cm, area of 𝐿𝐶𝐹=871.5cm

Q14:

In the figure, 𝐴𝐵𝐶𝐷 is a parallelogram with 𝐹 on 𝐵𝐶 and rays 𝐷𝐹 and 𝐴𝐵 meeting at 𝐸. Find the length of 𝐵𝐸.

Q15:

In the given parallelogram, 𝐷𝐸=2𝐸𝑀 and 𝐴𝐷=13cm. Determine 𝐹𝐷.

Q16:

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

Q17:

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

Q18:

If the perimeter of the parallelogram below is 39.6 cm, find the length of 𝑀𝐸.

Q19:

𝐴 𝐵 𝐶 𝐷 is a parallelogram, and 𝑋 is an interior point in it, where 𝐷𝑋 bisects angle 𝐴𝐷𝐶, and 𝐶𝑋 bisects angle 𝐷𝐶𝐵. If 𝑌 is the midpoint of 𝐷𝐶 and 𝑋𝑌=45cm, determine the length of 𝑌𝐶.

Q20:

Given that 𝐴𝐵𝐶𝐷 is a parallelogram, and 𝑚𝐶𝐷𝐸=40, determine 𝑚𝐴.

Q21:

Given that 𝐴𝐵𝐶𝐷 is a rectangle, and 𝐴𝐵𝐸𝐹 is a parallelogram, find the area of 𝑋𝐴𝐹.

Q22:

Given that 𝑋𝑀=21, 𝑋𝑁=24, and 𝑁𝑍=28, find 𝑋𝑌.

Q23:

Find the length of 𝐶𝐵.

Q24:

Determine 𝐶𝐸𝐸𝐴, if 𝐴𝐷𝐷𝐵=2922.

  • A 2 2 2 9
  • B 2 9 5 1
  • C 5 1 2 9
  • D 2 9 2 2

Q25:

Find the value of 𝑥.

  • A26
  • B19
  • C9
  • D21

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