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Constructing a Triangle Midsegment - Concept

Teacher/Instructor Brian McCall
Brian McCall

Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

A triangle mid segment is a line segment whose endpoints are the midpoints of a triangle. The triangle mid segment is parallel to the third side (the side that does not contain an endpoint). Also, the mid-segment is half the length of the third side.

A mid segment in a triangle, not a trapezoid, we're not going to talk about those right now, is a line segment that connects two midpoints of that triangle. It is similar to a median but it's not exactly the same. The difference between a median and a mid segment is that the mid segment does not contain the vertex as one of your endpoints.
So, if we have a triangle right here and you want to find a median, first thing you're going to have to is find the midpoint of that side. To connect it to the other midpoint you're going to have to find that midpoint and you could connect those and that would be one of your mid segments. There's going to be three mid segments in every triangle. If I find the midpoint of this third side I could connect those two midpoints and that would be a mid segment and I could connect those two points and that would be a mid segment. So every mid segment will be within the triangle and they will be three in every triangle.

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