Are triangles ADC and EBC congruent?

Question

Are triangles ADC and EBC congruent?

1. Yes, by SSS 
2. Yes, by AAS 
3. Yes, by SAS 
4. Not enough information

Answer 1

Angle CBD is congruent to itself, so triangles ADC and EBC are similar by AA similarity. Therefore, angles ADC and EBC are congruent because AA similarity confers AAA similarity.

Now we have AAS congruence (as well as ASA congruence).

Anewer (2) is the correct answer choice.