# Midsegment of a Triangle

- Author:
- Tim Brzezinski

Definition: A

**midsegment of a triangle**is a segment that connects the midpoints of any 2 sides of that triangle. Question: How many midsegments does a triangle have? Let's proceed: In the applet below, points D and E are midpoints of 2 sides of triangle ABC. One midsegment of Triangle ABC is shown in green. Move the vertices A, B, and C of Triangle ABC around. As you do, observe the two comments off to the right side. Then, answer the questions below the applet.Questions:
1) What do you notice about the slopes of segments DE and AB? What does this imply about these 2 segments?
2) What does the ratio of DE to AB tell us about the midsegment of any triangle?
3) If we refer to the black side of the triangle as the triangle's "3rd side", complete the following statement. Be sure to use the phrase "3rd side" in each blank below.

**The MIDSEGMENT of a triangle is ALWAYS i) ________________________________________________________________________, and ii) ________________________________________________________________________.**