# How to Use Split and Merge to Explore Constructions

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The Edit | Split/Merge commands are often useful when you’re investigating the behavior of a particular construction and you want to see what happens in the case of a slightly different construction. In this extended example, you’ll construct the diagonals of a general quadrilateral, and then investigate what happens when you turn the quadrilateral into a parallelogram, a rectangle, and a rhombus.

1. | To begin, construct quadrilateral ABCD, its two diagonals, and the point of intersection E of the diagonals. Then measure the distances and angle shown in the figure at right. Drag the vertices around to see if there’s any relationship between the various measurements.
2. | Now turn the quadrilateral into a parallelogram. Construct two parallel lines as shown at right: one through D parallel to the segment connecting A and B, and another through B parallel to the segment connecting A and D. Also construct the intersection of the parallels.
3. | Select both point C and the intersection, and choose Edit | Merge Points to merge the vertex with the intersection point.
4. | Hide the parallel lines. Then drag vertices A, B, and D. How are the measurements now related?
5. | Next turn the quadrilateral into a rectangle by making BAD into a right angle. Construct a perpendicular as shown at right and merge point D to the perpendicular. Again, drag the vertices and watch the measurements. Do you notice anything different?
6. | Finally, change your quadrilateral into a rhombus. First split D from the perpendicular. Then construct a circle centered at A and passing through B, and merge D to the circle. Drag the vertices once more to see what relationships the measurements now reveal.