Midsegment of a Triangle Worksheet
Explore the properties and theorems related to the midsegment of a triangle with this Grade 12 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. A midsegment of a triangle connects the of two sides of the triangle.
2. The Midsegment Theorem states that the midsegment is parallel to the side and is half the length of the side.
3. In triangle ABC, D is the midpoint of AB and E is the midpoint of AC. If BC = 18 cm, what is the length of DE?
4. If a midsegment of a triangle has a length of 7 cm, what is the length of the third side to which it is parallel?
3.5 cm
7 cm
14 cm
21 cm
5. Triangle XYZ has vertices X(1, 2), Y(5, 8), and Z(9, 4). Find the coordinates of the midpoints of sides XY and YZ, and then determine the length of the midsegment connecting these two midpoints. What is the length of XZ? Verify the Midsegment Theorem.
6. A triangle has only one midsegment.
True
False
7. The midsegment of a triangle is always longer than the side it is parallel to.
True
False
8. The perimeter of a triangle is 40 cm. If a triangle is formed by connecting the midpoints of the sides of the original triangle, what is the perimeter of this new (inner) triangle? Explain your reasoning.