Final answer:
A definitive proof of the congruence of ∆NQT and ∆SQR cannot be provided without additional context or a diagram, but the hints suggest potential congruence theorems that might apply if further information were available.
Step-by-step explanation:
Without additional context or a diagram, it's not possible to provide a rigorous mathematical proof for the congruence of ∆NQT and ∆SQR. However, the statement mentions that line ℓ bisects at Q, and angles ∠N and ∠S are congruent. These clues suggest that we might be dealing with triangles that share a common bisector and have a pair of congruent angles.
If the common bisector is an angle bisector or a side of both triangles, and the congruent angles imply that the triangles are sitting on the same base or have another pair of congruent sides, then one might be able to show that ∆NQT and ∆SQR are congruent using the Angle-Side-Angle (ASA) or Side-Angle-Side (SAS) congruence theorems, or possibly another theorem depending on the specific situation.
However, with the current information, it's not possible to definitively prove the congruence of these triangles. A complete and accurate proof would require a precise definition of the way line ℓ relates to both triangles and more information about their sides and angles.