Answer:
Explanation:
In order to prove that Triangle BCA is congruent to Triangle DCE, we must show that all corresponding sides and angles of both triangles are congruent.
Given that line segment AB is congruent to line segment CD (AB ≅ CD) and line segment AC is congruent to line segment CE (AC ≅ CE), we can say that both triangles share a side of equal length, and they also share an angle at point C.
Now we need to show that angle BCA is congruent to angle DCE. Since we know that line segment AB is congruent to line segment CD, we can say that angle ABC is congruent to angle DCE (by the Angle-Side-Angle Congruence Theorem).
Therefore, we have proved that Triangle BCA is congruent to Triangle DCE by the Side-Angle-Side Congruence Theorem (SAS), which states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.