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Lesson: Trapezoid Midsegment Theorem

In this lesson, we will learn how to find unknown lengths in trapezoids using the midsegment of a trapezoid theorem.

Sample Question Videos

02:24

Worksheet • 13 Questions • 1 Video

Q1:

In the figure, 𝐿 𝐻 is the midsegment of trapezoid 𝐹 𝐺 𝐽 𝐾 . What is the value of π‘₯ ?

Q2:

In the figure, 𝐿 𝐻 is the midsegment of trapezoid 𝐹 𝐺 𝐽 𝐾 . What is the value of π‘₯ ?

Q3:

In the figure, 𝐿 𝐻 is the midsegment of trapezoid 𝐹 𝐺 𝐽 𝐾 . What is the value of π‘₯ ?

Q4:

In a trapezium 𝐴 𝐡 𝐢 𝐷 where 𝐴 𝐷 β«½ 𝐡 𝐢 , the point 𝑋 is the midpoint of 𝐴 𝐡 , π‘Œ is the midpoint of 𝐷 𝐢 , and 𝑋 π‘Œ = 2 7 c m . The area of the trapezium is 513 cm2 and 𝐡 𝐢 = 2 9 c m .

Find the length of 𝐴 𝐷 and the perpendicular distance between 𝐴 𝐷 and 𝐡 𝐢 .

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

Q5:

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

Q6:

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

Q7:

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

Q8:

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

Q9:

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

Q10:

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

Q11:

Suppose that 𝐴 𝐡 = 1 2 8 and 𝑋 π‘Œ = 9 5 . What is 𝐢 𝐷 ?

  • A62
  • B111.5
  • C95
  • D128

Q12:

Suppose that 𝐴 𝐡 = 1 6 8 and 𝑋 π‘Œ = 1 4 9 . What is 𝐢 𝐷 ?

  • A130
  • B158.5
  • C149
  • D168

Q13:

Suppose that 𝐴 𝐡 = 1 9 6 and 𝑋 π‘Œ = 1 7 7 . 5 . What is 𝐢 𝐷 ?

  • A159
  • B186.8
  • C177.5
  • D196
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