The two triangles AEB and DCB are congruent by Side-Side-Side (SSS) theorem.
Two or more triangles are said to be congruent if and only if their corresponding sides and measure of internal angles are equal. Thus the corresponding properties of the triangles are equal in all respect.
The required statements and reasons for the proof are given below:
Statements Reasons
1. <A ≅ <D Given
2. AE ≅ DC Given
3. EB ≅ CB Given
4. BA ≅ BD Given
5. <ABE ≅ <CBD Angle reflexive property
5. ΔAEB ≅ ΔDCB Side Side Side (SSS) Theorem
Therefore it can be concluded that triangles AEB and DCB are congruent by Side-Side-Side (SSS) theorem.