Lesson Worksheet: Trapezoid Midsegment Theorem Mathematics

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?

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.

  • A𝐾𝐹=50cm
  • B𝐾𝐹=100cm
  • C𝐾𝐹=312cm
  • D𝐾𝐹=24.98cm
  • E𝐾𝐹=25cm

Q4:

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

Q5:

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

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

  • A𝐴𝐷=25cm, distance is 19 cm
  • B𝐴𝐷=83cm, distance is 17.7 cm
  • C𝐴𝐷=25cm, distance is 20.5 cm
  • D𝐴𝐷=83cm, distance is 19 cm
  • E𝐴𝐷=83cm, 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.

  • A𝐾𝐹=22cm
  • B𝐾𝐹=44cm
  • C𝐾𝐹=60cm
  • D𝐾𝐹=10.95cm
  • E𝐾𝐹=11cm

Q9:

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

  • A𝐾𝐹=58cm
  • B𝐾𝐹=116cm
  • C𝐾𝐹=408cm
  • D𝐾𝐹=28.57cm
  • E𝐾𝐹=29cm

Q10:

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

Q11:

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

Q12:

Suppose that 𝐴𝐵=168 and 𝑋𝑌=149. What is 𝐶𝐷?

Q13:

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

Q14:

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

Q15:

True or False: The midsegment of a trapezoid is a line that goes across from any point on one leg to the midpoint of the other leg; its length is equal to half the sum of the lengths of the two bases of the trapezoid.

  • AFalse
  • BTrue

Q16:

𝐴𝐵𝐶𝐷 is a trapezoid, where 𝐴𝐵𝐶𝐷. 𝑋𝑌 is connecting the midpoints of legs 𝐴𝐷 and 𝐵𝐶. If 𝐴𝐵=7𝑥+15, 𝐶𝐷=2𝑥+4, and 𝑋𝑌=23, find the value of 𝑥.

  • A3
  • B13
  • C49
  • D94
  • E18

Q17:

Which of the following is the correct formula to measure the length of 𝑋𝑌 in the trapezoid shown, using the trapezoid midsegment theorem?

  • A𝐶𝐷=𝑋𝑌+𝐴𝐵2
  • B𝑋𝑌=𝐶𝐷+𝐴𝐵2
  • C𝑋𝑌=𝐶𝐷+𝐴𝐵
  • D𝐴𝐵=𝑋𝑌+𝐶𝐷
  • E𝐴𝐵=𝑋𝑌+𝐶𝐷2

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