We want to write a two-column proof where the triangles ABC and EDC are congruent. We are told that two sides of △ ABC which are AB and CA are congruent to two sides of △ EDC which are ED and CE, respectively. Also, by definition of a segment bisector, C is the midpoint of BD which implies BC ≅ CD. Let's then mark the congruent sides in the given diagram.
Given this information, we know that the congruent sides can be expressed as follows.
AB ≅ ED
AC ≅ EC
BC ≅ DC
Since we are dealing with the relationship between three sides of the triangles, we ought to consider which theorem concerning triangle congruence that we should use. Let's recall the Side-Side-Side (SSS) Congruence Postulate.
Side-Side-Side Congruence Postulate
If the three sides of a triangle are congruent to the three sides of another triangle, then the triangles are congruent.
Well, according to the Side-Side-Side Congruence Postulate, we can conclude that △ ABC is congruent to △ EDC. We can summarize this proof by making a two-column proof. To make this happen, we will create a table by writing the statements in the first column and we will write the reasons behind the statements in the second column.
