Theorem

1
Section 5.4

• Theorem MIDSEGMENT THEOREM
• The segment connecting the midpoints of two sides
  of a triangle is parallel to the third side and
  is half as long.

2
How to prove is a segment is a midsegment

• Sketch the triangle/plot the points
• Use the midpoint formula to find the midpoints of
  the sides
• Use the slope formula to find the slopes of the
  potential midsgements and opposite sides
• Confirm that the slopes of the potential
  midsegment and the side are the same
• Use the distance formula to calculate the length
  of the possible midsegment and opposite side
• Confirm the length of the potential midsegment is
  half as long as the opposite side

x1 x2 , y1 y2 2 2
Distance Formula
The midpoint formula
AB v (x2 x1)2 (y2 y1)2