Triangle BCA is congruent to triangle DCE due to the Side-Angle-Side (SAS) Postulate, since two sides are congruent and they share a common base, which serves as the included angle.
To determine why triangle BCA is congruent to triangle DCE, we must examine the given conditions and apply the congruence postulates and theorems of geometry.
If segment AC is congruent to segment CE, and segment BC is congruent to segment DC, we can say that two sides of the triangles are congruent. Since segment BC is shared by both triangles (BC is a common side), it serves as the base for both triangles BCA and DCE.
Consequently, we have two sides and the included angle equal, which follows the Side-Angle-Side (SAS) Postulate for triangle congruence.
Therefore, we can conclude that triangle BCA is congruent to triangle DCE based on the SAS Postulate.