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? ACB=ECD BC=DC AB=ED A=E

Answer 1

To use the SAS (Side-Angle-Side) congruence theorem to conclude that triangles ABC and EDC are congruent, we need two sides and the angle between those sides in one triangle to be congruent to the corresponding two sides and the angle between them in the other triangle.

Given that point C is the midpoint of both segments BD and AE, you already know that:

1. ACB = ECD (corresponding angles)
2. AB = ED (one pair of corresponding sides)
3. BC = DC (the other pair of corresponding sides)

To apply the SAS theorem correctly, the crucial additional information needed is to confirm that the angles ACB and ECD are indeed congruent. This will suffice for us to state that triangles ABC and EDC are congruent:

• You need to establish that ACB = ECD (the angle formed by the sides AC and BC is equal to the angle formed by the sides EC and DC).

With that specific angle congruence, plus the congruence of the two sides (AB = ED and BC = DC), you can use the SAS theorem to conclude that triangle ABC is congruent to triangle EDC.

Answer 2

Choose one

Answer 3

To apply the SAS congruence theorem correctly and conclude that triangles ABC and EDC are congruent, the additional information you need is:

ACB = ECD (the angles must be congruent).