To determine if the triangles are congruent by the Angle-Side-Angle (ASA) criterion, you need to have two angles and the included side between them congruent in both triangles.
From the information provided, we have:
- \( AB \cong AD \) (one side is congruent)
- \( \angle ABC \cong \angle ADC \) (an angle is congruent)
- \( CB \cong CD \) (another side is congruent)
- \( \angle ACB \cong \angle ACD \) (another angle is congruent)
For ASA, you actually need two angles and the side between them to be congruent.
In order to state that the triangles are congruent by ASA, we need to ensure that the side we have (\( AB \) and \( AD \) or \( CB \) and \( CD \)) is the included side between the two angles.
Here’s what you would specifically need:
- You would need to establish if \( AB \) and \( AD \) are the sides between \( \angle ABC \) and \( \angle ACB \) (to use the angles \( \angle ABC \) and \( \angle ACB \)).
- Alternatively, if you wish to use angles \( \angle ADC \) and \( \angle ACD \), you would need to establish that \( AD \) and \( AC \) are included between \( \angle ADC \) and \( \angle ACD \).
In summary, for ASA, you need:
- Two angles that are congruent, and
- The side that is included between them to be congruent.
Thus, based on the information you currently have, you would need to clarify which side is included between the angles you mentioned to establish congruence using ASA.