Worksheet: Trapezoid Midsegment Theorem

In this worksheet, we will practice finding unknown lengths in trapezoids using the midsegment of a trapezoid theorem.

Q1:

Suppose that 𝐴 𝐵 = 1 2 8 and 𝑋 𝑌 = 9 5 . What is 𝐶 𝐷 ?

  • A128
  • B111.5
  • C95
  • D62

Q2:

In the figure, 𝐿 𝐻 is the midsegment of trapezoid 𝐹 𝐺 𝐽 𝐾 . What is the value of 𝑥 ?

Q3:

If 𝐵 𝐴 = 2 4 c m and 𝐷 𝐶 = 2 6 c m , find the length of 𝐾 𝐹 .

Q4:

Find the length of the middle base of a trapezium whose parallel bases are 107 cm and 246 cm.

Q5:

In a trapezium 𝐴 𝐵 𝐶 𝐷 where 𝐴 𝐷 𝐵 𝐶 , the point 𝑋 is the midpoint of 𝐴 𝐵 , 𝑌 is the midpoint of 𝐷 𝐶 , and 𝑋 𝑌 = 2 7 c m . The area of the trapezium is 513 cm2 and 𝐵 𝐶 = 2 9 c m .

Find the length of 𝐴 𝐷 and the perpendicular distance between 𝐴 𝐷 and 𝐵 𝐶 .

  • A 𝐴 𝐷 = 2 5 c m , distance is 20.5 cm
  • B 𝐴 𝐷 = 8 3 c m , distance is 17.7 cm
  • C 𝐴 𝐷 = 8 3 c m , distance is 6.2 cm
  • D 𝐴 𝐷 = 2 5 c m , distance is 19 cm
  • E 𝐴 𝐷 = 8 3 c m , distance is 19 cm

Q6:

In the figure, 𝐿 𝐻 is the midsegment of trapezoid 𝐹 𝐺 𝐽 𝐾 . What is the value of 𝑥 ?

Q7:

In the figure, 𝐿 𝐻 is the midsegment of trapezoid 𝐹 𝐺 𝐽 𝐾 . What is the value of 𝑥 ?

Q8:

If 𝐵 𝐴 = 1 0 c m and 𝐷 𝐶 = 1 2 c m , find the length of 𝐾 𝐹 .

Q9:

If 𝐵 𝐴 = 3 4 c m and 𝐷 𝐶 = 2 4 c m , find the length of 𝐾 𝐹 .

Q10:

Find the length of the middle base of a trapezium whose parallel bases are 14 cm and 46 cm.

Q11:

Find the length of the middle base of a trapezium whose parallel bases are 27 cm and 54 cm.

Q12:

Suppose that 𝐴 𝐵 = 1 6 8 and 𝑋 𝑌 = 1 4 9 . What is 𝐶 𝐷 ?

  • A168
  • B158.5
  • C149
  • D130

Q13:

Suppose that 𝐴 𝐵 = 1 9 6 and 𝑋 𝑌 = 1 7 7 . 5 . What is 𝐶 𝐷 ?

  • A196
  • B186.8
  • C177.5
  • D159

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