Answer:
Proved below
Explanation:
To Prove: Triangle AEB ≅ Triangle CEB.
Step 1
Statement: ABCD is a rhombus
Reason: Given.
Step 2
Statement: AC and BD bisects each other.
Reason: The diagonals of a rhombus bisects each other.
Step 3
Statement: AE ≅ EC
Reason: A segment bisector divides a segment into two congruent segments.
Step 4
Statement: AB ≅ BC
Reason: All sides of a rhombus are congruent.
Step 5
Statement: BE ≅ BE
Reason: Reflexive Property
Step 6
Statement: ∆ AEB ≅ ∆ CEB
Reason: SSS
The triangles are thus proved to be congruent.