1. Draw a large acute triangle. Select all three line segments and construct the midpoints.
2. Connect all the midpoints with a line segment.
3. Measure all the angles in the figure. Which ones are equal?
The figure you have should look something like this:
4. Do these angles remain equal to their corresponding angles if we take one of the vertices and move it?
5. Measure the slopes of several of the line segments. Which line segments have equal slope? Does this property change if you select one of the vertices and move it?