If point C is the midpoint of both BD and AE, what additional information would you need to be able to state that ABC=EDC by the SAS congruence theorem?

Answer 1

To apply the Side-Angle-Side (SAS) congruence theorem and conclude that triangles \( ABC \) and \( EDC \) are congruent, you need the following additional information:

1. One pair of congruent sides: You need to know that one of the sides \( AB \) is congruent to side \( ED \) (or one of the sides \( AC \) is congruent to side \( EC \)). This means you need to establish \( AB \cong ED \) or \( AC \cong EC \).

2. Included angle information: You need to ensure that the angle \( \angle ACB \) is congruent to \( \angle ECD \). This angle subtends the two sides you will designate as congruent in the triangles.

With these pieces of information—one side length pair being congruent and the angles between the respective pairs being congruent—you can use the SAS theorem to conclude that triangles \( ABC \) and \( EDC \) are congruent.