Final answer:
Triangles BAC and EDC are similar due to the Angle-Angle similarity criterion, which is satisfied by the congruency of corresponding angles formed by intersecting parallel lines.
Step-by-step explanation:
To prove that triangles BAC and EDC are similar, we must show that they have the same shape but not necessarily the same size. This is achieved by demonstrating that they have equal corresponding angles and that their corresponding sides are proportional. Given that BA is parallel to CA and CD is parallel to ED, we can use these parallel lines to find congruent angles.
Firstly, since BA is parallel to CA, angle BAC is congruent to angle EDC by alternate interior angles due to line BD intersecting the parallel lines. Similarly, since CD is parallel to ED, angle BCA is congruent to angle CED. Finally, by the Angle-Angle (AA) criterion, the two triangles are similar.
To summarize, triangles BAC and EDC are similar because they both share angle ACB, and the other two corresponding angles are congruent due to the parallel lines, which satisfy the Angle-Angle criterion for triangle similarity.