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How are three midsegments of any triangle related to each other?

A. They are congruent.
B. They are parallel.
C. They are perpendicular.
D. They are bisectors.

1 Answer

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Final answer:

The midsegments of a triangle are parallel to the sides of the triangle they do not touch and half their length. The midsegments are also parallel to each other, making option B (They are parallel) the correct answer.

Step-by-step explanation:

The midsegments of a triangle are related to each other in that they are parallel to the sides of the triangle they do not touch and they are half the length of those sides. This conforms to the Triangle Midsegment Theorem, which states that a segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long.

Since each midsegment is parallel to one side of the triangle, it can be inferred that the midsegments are parallel to each other. Option A and C from the given choices (congruent and perpendicular) do not hold true for midsegments. Midsegments are not the bisectors of the sides either, so option D is incorrect as well. Therefore, the correct answer is that the midsegments are parallel to each other, making option B the right choice.

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