To prove that triangle \( AABC \) is congruent to triangle \( AQRS \) by the ASA (Angle-Side-Angle) Congruence Theorem, you need the measures of two angles and the length of the side that is included between those two angles for both triangles.
Among the options provided:
- \( \angle ABE \equiv \angle QR \): This option states that an angle in triangle \( AABC \) is congruent to an angle in triangle \( AQRS \).
- \( \angle A < \angle Q \): This option is about inequality and does not help with congruence.
- \( \angle CEL \equiv \angle S \): This option states the congruence of another pair of angles.
- \( \angle ACE \equiv \angle QS \): This option states another angle congruence.
To utilize the ASA congruence theorem effectively, you need:
- Two angles from both triangles that are congruent.
- The side that is included between those two angles in both triangles must also be congruent.
However, based on the given options, the congruence of the angles between the two triangles must indeed involve a specific included side being congruent. Therefore, for the ASA criterion, if you need to select the most appropriate option, it should include both the congruence of two angles and the length of the side between those angles.
Since none of the options clearly state an included side being equal, the correct approach cannot be determined without further context about which angles correspond to which sides.
To conclude, you require two angles that are congruent and the corresponding side included between them as congruent in both triangles for the ASA theorem to apply. Make sure to check if there is information about side lengths in the context of your question, which is essential for the ASA criterion.
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