midsegment of a triangle
segment that connects the midpoints of two sides of a triangle
The midsegment of a triangle is a line segment connecting the midpoints of two sides of the triangle. It is also called the midline, because it splits the triangle into two halves of equal area.
Properties of the midsegment of a triangle:
– The length of the midsegment is half the length of the third side of the triangle.
– The midsegment is parallel to the third side of the triangle.
– The midsegment divides the triangle into two smaller triangles of equal area.
– The point where the midsegment intersects the third side is the midpoint of that side.
The midsegment theorem states that the length of the midsegment of a triangle is equal to half the sum of the lengths of the other two sides. This can be written as:
midsegment length = (1/2) x (sum of other two sides)
This theorem is useful in solving problems involving the midsegment of a triangle. For example, if you are given the length of the midsegment and one side of a triangle, you can use the midsegment theorem to find the length of the other side.
Overall, the midsegment of a triangle is an important concept in geometry that has many practical applications.
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