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
Distance Formula:
The midpoint formula:
AB = √ (x2 – x1)2 + (y2 – y1)2