Midsegment of a Triangle Worksheet
Explore the properties and theorems related to the midsegment of a triangle with this Grade 11 geometry worksheet.
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Midsegment of a Triangle
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. What is the relationship between a midsegment of a triangle and the third side?
It is perpendicular to the third side.
It is half the length of the third side.
It is twice the length of the third side.
It is congruent to the third side.
2. Which of the following is true about a midsegment of a triangle?
It connects a vertex to the midpoint of the opposite side.
It is parallel to the third side.
It bisects the angle from which it originates.
It is always longer than the third side.
1. The Midsegment Theorem states that the segment connecting the midpoints of two sides of a triangle is to the third side and is the length of the third side.
2. In triangle ABC, if D and E are midpoints of AB and AC respectively, then DE is a and is parallel to .
1. In ΔXYZ, M is the midpoint of XY and N is the midpoint of XZ. If MN = 7.5 cm, what is the length of YZ? Justify your answer.
2. In ΔPQR, the midpoints of PQ, QR, and RP are S, T, and U respectively. If PQ = 10, QR = 12, and RP = 14, find the perimeter of ΔSTU.
1. A triangle can have more than one midsegment.
True
False
1. Consider a triangle with vertices A(1, 2), B(7, 4), and C(3, 8). Find the coordinates of the midpoints of AB and AC. Then, find the length of the midsegment connecting these two midpoints and verify that it is half the length of BC.
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