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 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?

Q2:

Determine 𝐴𝐡𝐡𝐷, if 𝐴𝐷𝐷𝐡=3823.

  • A6123
  • B6138
  • C3861
  • D2361

Q3:

In the figure, 𝐷𝑋 and πΈπ‘Œ are parallel to 𝐴𝐢 and 𝐴𝐡 respectively. If 𝐡𝐢=12cm, 𝐴𝐷𝐷𝐡=2, and 𝐸𝐢=13𝐴𝐸, determine the length of π‘‹π‘Œ.

Q4:

Find the length of 𝐢𝐡.

Q5:

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

Q6:

If the perimeter of △𝐴𝐡𝐢=9.7cm, 𝐸 is the midpoint of 𝐴𝐢, and 𝐷𝐸βˆ₯𝐡𝐢, find the length of 𝐷𝐸.

Q7:

Given that 𝑍 is the midpoint of 𝐷𝐢, the perimeter of △𝐴𝐷𝐢 is 33 cm, 𝐴𝐷=7cm, and 𝑍𝐢=5cm, find the length of π΄π‘Œ.

Q8:

Given that 𝐴𝐸𝐹𝐷 is a parallelogram, where 𝐸 and 𝐹 are the midpoints of 𝐷𝐡 and 𝐷𝐢 respectively, find the length of 𝐢𝐡.

Q9:

Given that 𝐴𝐡𝐢𝐷 is a parallelogram, find π‘šβˆ π΅π΄πΈ.

Q10:

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

Q11:

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

Q12:

𝐹𝐷𝐸𝐢 is a parallelogram, where 𝐹 and 𝐷 are the midpoints of 𝐴𝐡 and 𝐴𝐢, respectively, and 𝐢𝐸=6cm. Determine the length of 𝐡𝐢.

Q13:

Given that the area of the parallelogram 𝐴𝐡𝐢𝐷=1,743cm and that of the △𝐴𝐹𝐷=268cm, find the area of 𝐹𝐡𝐢𝐿 and that of the △𝐿𝐢𝐹.

  • Aarea of 𝐹𝐡𝐢𝐿=1,475cm, area of △𝐿𝐢𝐹=871.5cm
  • Barea of 𝐹𝐡𝐢𝐿=1,743cm, area of △𝐿𝐢𝐹=871.5cm
  • Carea of 𝐹𝐡𝐢𝐿=435.75cm, area of △𝐿𝐢𝐹=1,475cm
  • Darea of 𝐹𝐡𝐢𝐿=1,475cm, area of △𝐿𝐢𝐹=435.75cm
  • Earea of 𝐹𝐡𝐢𝐿=871.5cm, area of △𝐿𝐢𝐹=1,475cm

Q14:

In the figure, 𝐴𝐡𝐢𝐷 is a parallelogram with 𝐹 on 𝐡𝐢 and rays 𝐷𝐹 and 𝐴𝐡 meeting at 𝐸. Find the length of 𝐡𝐸.

Q15:

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

Q16:

Given that 𝐴𝐡𝐢𝐷 is a parallelogram, find the length of π‘Œπ‘.

Q17:

Given that 𝐴𝐡𝐢𝐷 is a parallelogram, find the length of π‘Œπ‘.

Q18:

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

Q19:

𝐴𝐡𝐢𝐷 is a parallelogram, and 𝑋 is an interior point in it, where 𝐷𝑋 bisects angle 𝐴𝐷𝐢, and 𝐢𝑋 bisects angle 𝐷𝐢𝐡. If π‘Œ is the midpoint of 𝐷𝐢 and π‘‹π‘Œ=45cm, determine the length of π‘ŒπΆ.

Q20:

Given that 𝐴𝐡𝐢𝐷 is a parallelogram, and π‘šβˆ πΆπ·πΈ=40∘, determine π‘šβˆ π΄.

Q21:

Given that 𝐴𝐡𝐢𝐷 is a rectangle, and 𝐴𝐡𝐸𝐹 is a parallelogram, find the area of △𝑋𝐴𝐹.

Q22:

Given that 𝑋𝑀=21, 𝑋𝑁=24, and 𝑁𝑍=28, find π‘‹π‘Œ.

Q23:

Find the length of 𝐢𝐡.

Q24:

Determine 𝐢𝐸𝐸𝐴, if 𝐴𝐷𝐷𝐡=2922.

  • A2229
  • B5129
  • C2951
  • D2922

Q25:

Find the value of π‘₯.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.