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Worksheet: Applications of Parallel Lines in a Triangle

Q1:

Given that 𝐴 𝐸 𝐹 𝐷 is a parallelogram, where 𝐸 and 𝐹 are the midpoints of 𝐷 𝐡 and 𝐷 𝐢 respectively, find the length of 𝐢 𝐡 .

Q2:

Given that 𝐴 𝐡 𝐢 𝐷 is a parallelogram, find π‘š ∠ 𝐡 𝐴 𝐸 .

  • A 6 7 ∘
  • B 1 1 3 ∘
  • C 4 6 ∘
  • D 2 1 ∘

Q3:

Find the length of 𝐢 𝐡 .

Q4:

Find the length of 𝐢 𝐡 .

Q5:

If the perimeter of , is the midpoint of , and , find the length of .

Q6:

On the figure, 𝐴 𝐡 𝐢 𝐷 is a parallelogram whose diagonals intersect at 𝑀 , and 𝑋 is a point on 𝐴 𝐷 . If 𝑀 𝑋 = 3 8 , what is 𝐢 𝐷 ?

Q7:

Given that 𝐴 𝐡 𝐢 𝐷 is a parallelogram, find the length of 𝐷 𝐻 .

Q8:

𝐹 𝐷 𝐸 𝐢 is a parallelogram, where 𝐹 and 𝐷 are the midpoints of 𝐴 𝐡 and 𝐴 𝐢 , respectively, and 𝐢 𝐸 = 6 c m . Determine the length of 𝐡 𝐢 .

Q9:

Given that the area of the parallelogram 𝐴 𝐡 𝐢 𝐷 = 1 7 4 3 c m 2 and that of the β–³ 𝐴 𝐹 𝐷 = 2 6 8 c m 2 , find the area of 𝐹 𝐡 𝐢 𝐿 and that of the β–³ 𝐿 𝐢 𝐹 .

  • A area of 𝐹 𝐡 𝐢 𝐿 = 1 4 7 5 c m 2 , area of β–³ 𝐿 𝐢 𝐹 = 4 3 5 . 7 5 c m 2
  • B area of 𝐹 𝐡 𝐢 𝐿 = 8 7 1 . 5 c m 2 , area of β–³ 𝐿 𝐢 𝐹 = 1 4 7 5 c m 2
  • C area of 𝐹 𝐡 𝐢 𝐿 = 4 3 5 . 7 5 c m 2 , area of β–³ 𝐿 𝐢 𝐹 = 1 4 7 5 c m 2
  • D area of 𝐹 𝐡 𝐢 𝐿 = 1 4 7 5 c m 2 , area of β–³ 𝐿 𝐢 𝐹 = 8 7 1 . 5 c m 2
  • E area of 𝐹 𝐡 𝐢 𝐿 = 1 7 4 3 c m 2 , area of β–³ 𝐿 𝐢 𝐹 = 8 7 1 . 5 c m 2

Q10:

In the figure, 𝐴 𝐡 𝐢 𝐷 is a parallelogram with 𝐹 on 𝐡 𝐢 and rays  𝐷 𝐹 and  𝐴 𝐡 meeting at 𝐸 . Find the length of 𝐡 𝐸 .

Q11:

In the given parallelogram, 𝐷 𝐸 = 2 𝐸 𝑀 and 𝐴 𝐷 = 1 3 c m . Determine 𝐹 𝐷 .

Q12:

Given that 𝑍 is the midpoint of 𝐷 𝐢 , the perimeter of β–³ 𝐴 𝐷 𝐢 is 33 cm, 𝐴 𝐷 = 7 c m , and 𝑍 𝐢 = 5 c m , find the length of 𝐴 π‘Œ .

Q13:

Determine , if .

  • A
  • B
  • C
  • D

Q14:

Determine , if .

  • A
  • B
  • C
  • D

Q15:

Given that 𝐴 𝐡 𝐢 𝐷 is a parallelogram, find the length of π‘Œ 𝑍 .

Q16:

If , , and , find the length of .

Q17:

Given that 𝐴 𝐡 𝐢 𝐷 is a parallelogram, find the length of π‘Œ 𝑍 .

Q18:

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

Q19:

In the figure, 𝐷 𝑋 and 𝐸 π‘Œ are parallel to 𝐴 𝐢 and 𝐴 𝐡 respectively. If 𝐡 𝐢 = 1 2 c m , 𝐴 𝐷 𝐷 𝐡 = 2 , and 𝐸 𝐢 = 1 3 𝐴 𝐸 , determine the length of 𝑋 π‘Œ .

Q20:

In the figure, 𝐷 𝑋 and 𝐸 π‘Œ are parallel to 𝐴 𝐢 and 𝐴 𝐡 respectively. If 𝐡 𝐢 = 1 6 c m , 𝐴 𝐷 𝐷 𝐡 = 7 9 , and 𝐸 𝐢 = 1 3 𝐴 𝐸 , determine the length of 𝑋 π‘Œ .

Q21:

𝐴 𝐡 𝐢 𝐷 is a parallelogram, and 𝑋 is an interior point in it, where  𝐷 𝑋 bisects angle 𝐴 𝐷 𝐢 , and  𝐢 𝑋 bisects angle 𝐷 𝐢 𝐡 . If π‘Œ is the midpoint of 𝐷 𝐢 and 𝑋 π‘Œ = 4 5 c m , determine the length of π‘Œ 𝐢 .

Q22:

Given that is a parallelogram, and , determine .

  • A
  • B
  • C
  • D

Q23:

In the figure, segments 𝑋 π‘Œ and 𝐡 𝐢 are parallel. If 𝐴 𝑋 = 1 8 , 𝑋 𝐡 = 2 4 , and 𝐴 π‘Œ = 2 7 , what is the length of π‘Œ 𝐢 ?

Q24:

In the figure, segments 𝑋 π‘Œ and 𝐡 𝐢 are parallel. If 𝐴 𝑋 = 3 0 , 𝑋 𝐡 = 1 8 , and 𝐴 π‘Œ = 2 0 , what is the length of π‘Œ 𝐢 ?