Discovering the Mid-Segment Property of Triangles
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The following discovery activity can be done prior to introducing the length of a mid-segment of a triangle or as a reinforcement of the property.  The activity can be done in groups or individually.


Task:  To discover the relationship between the length of the mid-segment and the length of the third side of the triangle.

Materials:
paper, compass, straight-edge, ruler.

Steps:

  1. Using a straight-edge, draw a triangle.
  2. Using a compass, bisect each side of the triangle to locate the midpoint of each side.
  3. Connect the midpoints to form the three mid-segments.
  4. Measure the mid-segments and the third sides for each pairing.  Record the lengths.

 Data:

DE =                 BC =
EF = AC =
FD = BA =
Record the data and make a conjecture regarding the relationship between the length of the mid-segment and the length of the third side of the triangle.