The mistake Lenny made in his proof is that he incorrectly labeled the angles in his explanation regarding the right angles formed by the perpendicular bisector. Specifically, he states that ∠MLI and ∠MLJ are right angles, but it should be stated that ∠LMI and ∠LMJ are the right angles formed by the perpendicular bisector.
Therefore, the correct response is:
The definition of a perpendicular bisector tells you that ∠LMI and ∠LMJ are right angles, not that ∠MLI and ∠MLJ are right angles.
This error affects the clarity of the proof and the relationships he describes regarding the triangles and the use of congruence.