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, 𝐴 𝐵 𝐶 𝐷 and 𝐷 𝐵 𝐶 𝐻 are two parallelograms having the same base 𝐶 𝐵 . Find the length of 𝐿 𝑀 .

Q2:

The perimeter of square 𝐴 𝐵 𝐶 𝐷 is 352. Find 𝐴 𝐹 .

Q3:

Given that 𝐷 and 𝐸 are the midpoints of 𝐴 𝐵 and 𝐴 𝐶 respectively, 𝐴 𝐷 = 3 2 c m , 𝐴 𝐸 = 1 9 c m , and 𝐷 𝐸 = 3 9 c m , determine the perimeter of 𝐷 𝐵 𝐶 𝐸 .

Q4:

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

  • A yes
  • B no

Q5:

Calculate the perimeter of 𝐷 𝐸 𝐶 𝐹 .

Q6:

In the figure shown, 𝐸 , 𝐹 , and 𝐷 are the midpoints of 𝐵 𝐶 , 𝐴 𝐵 , and 𝐴 𝐶 , respectively. Find the perimeter of 𝐸 𝐹 𝐷 .

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