In the diagram below, ABCD is a rhombus and the diagonal AC intersects the y-axis at E. Show that triangle AEB is congruent to triangle AED. Answer ___

1. State the equal sides from the definition of a rhombus.

Since $ABCD$ is a rhombus, all its sides are equal. Hence
$AB=AD.$

2. State the equal segments from the diagonals of a rhombus bisecting each other.

The diagonals of a rhombus bisect each other. Since $AC$ and $BD$ intersect at $E$,
$BE=DE.$

3. Use the common side and conclude congruence by SSS.

Also,
$AE=AE$
(common side). Therefore, the three corresponding sides are equal:
$AB=AD,\quad BE=DE,\quad AE=AE.$
Hence
$\triangle AEB \cong \triangle AED \quad \text{by SSS}.$