Relating Diagonal Midpoints and Side Slopes
Investigate how the slopes of a quadrilateral's sides relate to the midpoints of its diagonals.
Tarea 1
Putting It All Together
Answer these open ended questions on your own or with others to form deeper math connections.
Tarea 2
Move one vertex of the quadrilateral until the midpoints of the diagonals coincide with each other. What is the resulting shape? Try this with several different quadrilaterals. Can you make a hypothesis about the quadrilateral if the diagonals bisect each other? How could you verify this hypothesis using coordinate geometry?
Tarea 3
Check the "Keep opposite sides parallel" box to restrict point movement so that the opposite sides are always parallel. What do you notice about the midpoints of the diagonals? Move the vertices to try this with several different parallelograms. Can you make a hypothesis about the diagonals of a parallelogram? How could you verify this hypothesis using coordinate geometry?