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Mid-Segment of a Triangle
Definition:
The mid-segment of a triangle (also called a midline) is a segment joining the midpoints of two sides of a triangle.
Properties:
- The mid-segment of a triangle joins the midpoints of two sides of a triangle such that it is parallel to the third side of the triangle.
- The mid-segment of a triangle joins the midpoints of two sides of a triangle such that its length is half the length of the third side of the triangle.
Examples:
- Given DE is the length of the mid-segment. Find AB.
Solution:
The mid-segment is half of the third side.
7 is half of 14.
AB = 14. - Given DE, DF, and FE are the lengths of mid-segments. Find the perimeter of triangle ABC.
Solution:
The mid-segment is half of the third side.
6 is half of 12 so AC = 12
7 is half of 14 so CB = 14
8 is half of 16 so AB = 16
The perimeter of the large triangle ABC is:
12 + 14 + 16 = 42. - .
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