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.

Q1:

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

Q2:

The perimeter of square 𝐴𝐵𝐶𝐷 is 352. Find 𝐴𝐹.

Q3:

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.

Q4:

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

  • Ano
  • Byes

Q5:

Calculate the perimeter of 𝐷𝐸𝐶𝐹.

Q6:

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

Q7:

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

Q8:

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

Q9:

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

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

Q10:

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

Q11:

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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