Here is a rhombus:

1. What is true about the lengths of the sides of this figure? What else is true about AB and DC? About AD and BC?

2. Construct a diagonal in the figure above. Argue that the diagonal bisects the corner angles it intersects.

3. Construct a second diagonal in the figure above and label the point of intersection E. In addition to creating vertical angles, what else is true about the angles formed by the intersection of the two diagonals? Argue your claim below.