Midsegment of a Triangle
Overview
A midsegment connects the midpoints of two sides of a triangle, and it has two dependable properties: it is parallel to the third side, and its length is exactly one half the length of that third side. This lesson uses those two facts to find unknown lengths, including lengths written as algebraic expressions, and looks at what happens when all three midsegments are drawn at once — they form a smaller triangle whose sides are half the sides of the original.
Vocabulary
- Midpoint
- The point on a segment that divides it into two congruent segments.
- Midsegment of a Triangle
- A segment that joins the midpoints of two sides of a triangle.
- Parallel Lines
- Lines that lie in the same plane and do not intersect.
- Third Side
- The side of the triangle that a midsegment does not touch; the midsegment is parallel to this side and half its length.
Main Ideas
- A midsegment is parallel to the third side of the triangle.
- A midsegment measures one half the length of the third side, so the third side is twice the midsegment.
- The three midsegments of a triangle form four congruent triangles, and the triangle formed by the three midsegments has half the perimeter of the original triangle.
- Because a midpoint splits a side into two equal parts, a side with a midpoint marked gives an equation: the two halves are equal, and the whole side is twice either half.
- With variables on the coordinate plane, the same relationships hold in terms of the variables — answers may be expressions, not numbers.
Lesson Notes
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Lesson Video
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Practice Problems
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Download the practice worksheet for this lesson, work the problems, then check your work with the solutions.