Based on the triangle midsegment theorem, the missing parts are:
Slope of DE = 0
Slope of BC = 0
Because the slopes are equal, then DE∥BC.
What is the Triangle Midsegment Theorem?
According to the triangle midsegment theorem, the segment that joins the midpoints of two sides of a triangle is parallel to the third side of the triangle.
If the slope of two lines are the same, it implies they are parallel to each other. In the proof shown in the diagram below, the missing parts that proves that DE and BC are parallel are:
Slope of DE = 0
Slope of BC = 0
Because the slopes are equal, then DE∥BC.
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