Worksheet: Trapezoid Midsegment Theorem

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

Q1:

Suppose that 𝐴𝐵=128 and 𝑋𝑌=95. What is 𝐶𝐷?

  • A111.5
  • B128
  • C95
  • D62

Q2:

In the figure, 𝐿𝐻 is the midsegment of trapezoid 𝐹𝐺𝐽𝐾. What is the value of 𝑥?

Q3:

If 𝐵𝐴=24cm and 𝐷𝐶=26cm, find the length of 𝐾𝐹.

Q4:

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

Q5:

In a trapezium 𝐴𝐵𝐶𝐷 where 𝐴𝐷𝐵𝐶, the point 𝑋 is the midpoint of 𝐴𝐵, 𝑌 is the midpoint of 𝐷𝐶, and 𝑋𝑌=27cm. The area of the trapezium is 513 cm2 and 𝐵𝐶=29cm.

Find the length of 𝐴𝐷 and the perpendicular distance between 𝐴𝐷 and 𝐵𝐶.

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

Q6:

In the figure, 𝐿𝐻 is the midsegment of trapezoid 𝐹𝐺𝐽𝐾. What is the value of 𝑥?

Q7:

In the figure, 𝐿𝐻 is the midsegment of trapezoid 𝐹𝐺𝐽𝐾. What is the value of 𝑥?

Q8:

If 𝐵𝐴=10cm and 𝐷𝐶=12cm, find the length of 𝐾𝐹.

Q9:

If 𝐵𝐴=34cm and 𝐷𝐶=24cm, find the length of 𝐾𝐹.

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 𝐴𝐵=168 and 𝑋𝑌=149. What is 𝐶𝐷?

  • A158.5
  • B168
  • C149
  • D130

Q13:

Suppose that 𝐴𝐵=196 and 𝑋𝑌=177.5. What is 𝐶𝐷?

  • A186.8
  • B196
  • C177.5
  • D159

Q14:

If the area of a trapezium is 1,377 cm2, and its height is 51 cm, find the length of its middle base.

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