Worksheet: Triangle Midsegment Theorem and Its Converse

In this worksheet, we will practice using the triangle midsegment theorem to prove parallelism of lines in a triangle or find a missing side length.


In the figure below, 𝐴𝐵𝐶𝐷 and 𝐷𝐵𝐶𝐻 are two parallelograms having the same base 𝐶𝐵. Find the length of 𝐿𝑀.


The perimeter of square 𝐴𝐵𝐶𝐷 is 352. Find 𝐴𝐹.


Given that 𝐷 and 𝐸 are the midpoints of 𝐴𝐵 and 𝐴𝐶 respectively, 𝐴𝐷=32cm, 𝐴𝐸=19cm, and 𝐷𝐸=39cm, determine the perimeter of 𝐷𝐵𝐶𝐸.


Is the line segment between the midpoints of two sides of a triangle parallel to the other side?

  • Ano
  • Byes


Calculate the perimeter of 𝐷𝐸𝐶𝐹.


In the figure shown, 𝐸, 𝐹, and 𝐷 are the midpoints of 𝐵𝐶, 𝐴𝐵, and 𝐴𝐶, respectively. Find the perimeter of 𝐸𝐹𝐷.


In the figure, 𝐴𝐵𝐶𝐷 is a square. If 𝐴𝐶=34, what is the length of 𝑋𝑌?


Find the values of 𝑥 and 𝑦.

  • A𝑥=3.75, 𝑦=7.75
  • B𝑥=5, 𝑦=7
  • C𝑥=5, 𝑦=14
  • D𝑥=3.33, 𝑦=11.33


Use the figure to determine the values of 𝑥 and 𝑦.

  • A15, 10
  • B8, 1
  • C8, 3
  • D15, 3


Given that 𝐶𝐵=12.8cm, determine the length of 𝑋𝑌.


Find the values of 𝑥 and 𝑦.

  • A𝑥=13, 𝑦=5
  • B𝑥=5, 𝑦=3
  • C𝑥=11, 𝑦=3
  • D𝑥=21, 𝑦=13

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