Answer
1. The kite creates two triangles. The bottom two triangles share a side, which is congruent to itself by the identity property.
2. The other two sides of the bottom two triangles are congruent because it is a kite.
3. To form a congruent triangle by ASA, this means that the triangles must have congruent angles, which only happens if the diagonals bisect both of angles.
4. If the triangles were not congruent, then the corresponding sides would not be congruent.
5. Corresponding sides are always congruent for kites.
6. Thus, the diagonals bisect both angles they go through.
7. Since all rhombuses are kites, the diagonal of a rhombus bisects the two angles it goes through.
