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Triangle Midsegment Properties - 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 midsegment is the line segment connecting the midpoints of two sides of a triangle. Since a triangle has three sides, each triangle has three midsegments. A triangle midsegment is parallel to the third side of the triangle and is half of the length of the third side. Another important set of polygon midsegment properties to be familiar with are trapezoid midsegment properties.

When we're talking about triangle midsegment there are 2 key things to keep in mind the first is what is a midegment? Well if I found the midpoint of one side of a triangle, if I found the midpoint of another side of the triangle and if I connected these with a line segment that is the definition of a midsegment, something that connects 2 midpoints of a triangle. So the first key thing about this segment right here is that it's going to be parallel to the third side.
Well how do I know which is the third side? It's going to be the side that is not involved in the end points of our midsegment, so this side right here doesn't have an endpoint of this midsegment. So I'm going to say that these two lines must be parallel, the second key thing about this midsegment is that it's going to be half of the length of the third side. So if I said this midsegment was 10 inches, then the length of this third side would be twice that 20 inches. But there's not just 1 triangle midsegment, there's going to be 3 and we'll find the other 2 by finding the midpoint of this third side. So if I connected these 2 midpoints I would have a midsegment that is parallel to this third side. So I'm going to use 2 arrows to show that these 2 are parallel. This midsegment will be half the length of this third side. And the third midsegment that I could draw is this midsegment right here which will be parallel to this third side so I'm going to use a different number of arrows to show that they're parallel. So I'm going to use 3 arrows I'm going to come up here 1, 2, 3. So we have 3 pairs of parallel sides with the midsegments and the other key thing is that midsegment is half the length of the third side.

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