In order to state that the triangles are congruent by the Angle-Side-Angle (ASA) criterion, we need to verify that we have two angles and the included side between them that are congruent in both triangles. According to the information provided:
- AB is congruent to AD (this is one side)
- angle ABC is congruent to angle ADC (this is one angle)
- CB is congruent to CD (this is another side)
- angle AVB is congruent to angle ACD (this is another angle)
Now, we need to identify which two angles are included with the congruent sides to form two triangles. To apply ASA, we would need:
- One of the angles (AB or AD should be adjacent to the corresponding side).
- The side between those angles to be congruent.
For example, if we had triangle ABC and triangle ADC, we need to confirm that the pair of congruent angles (angle ABC and angle ADC) are the included angles between the corresponding sides (AB and AD) which are congruent.
It appears that you have provided an additional congruent angle (angle AVB and angle ACD) and an additional congruent side (CB and CD) which indicates that you might be describing two triangles that are congruent from different angles.
To clarify the scenario, please ensure the following:
- Identify which triangles (e.g., triangle ABC and triangle ADC) we are comparing.
- Confirm that the angles being compared (angle ABC and angle ADC) are indeed the angles associated with the sides (AB and AD).
If you can provide this clarification, one can determine the congruence of the triangles by ASA.
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