enny wrote a paragraph proof of the Perpendicular Bisector Theorem. What mistake did Lenny make in his proof? HK¯¯¯¯¯¯¯¯¯ is a perpendicular bisector of IJ¯¯¯¯¯¯ , and L is the midpoint of IJ¯¯¯¯¯¯ . M is a point on the perpendicular bisector, HK¯¯¯¯¯¯¯¯¯ . By the definition of a perpendicular bisector, I know that IM¯¯¯¯¯¯¯¯≅JM¯¯¯¯¯¯¯¯ . By the definition of a perpendicular bisector, I also know that ∠MLI and ∠MLJ are right angles. ∠MLI≅∠MLJ because of the Right Angle Congruence Theorem. I can also say that ML¯¯¯¯¯¯¯¯¯≅ML¯¯¯¯¯¯¯¯¯ by the Reflexive Property of Congruence. With this information, I know that △MLI≅△MLJ by the SAS Congruence Theorem. Since the triangles are congruent, the CPCTC Theorem allows me to know that IL¯¯¯¯¯¯≅JL¯¯¯¯¯¯¯ . Knowing that these segments are congruent proves the Perpendicular Bisector Theorem. (1 point) Responses The definition of a perpendicular bisector tells you that IL¯¯¯¯¯¯≅JL¯¯¯¯¯¯¯ , not that IM¯¯¯¯¯¯¯¯≅JM¯¯¯¯¯¯¯¯ . The definition of a perpendicular bisector tells you that line segment cap i liters is congruent to line segment cap j liters, not that line segment cap i cap m is congruent to line segment cap j cap m. The definition of a perpendicular bisector tells you that∠LMI and ∠LMJ are right angles, not that ∠MLI and ∠MLJ are right angles. The definition of a perpendicular bisector tells you that ∠LMI and ∠LMJ are right angles, not that ∠MLI and ∠MLJ are right angles. The SAS Congruence Theorem tells you that △MLI≅△JLM , not that △MLI≅△MLJ . The SAS Congruence Theorem tells you that △MLI≅△JLM , not that △MLI≅△MLJ . Lenny did not make a mistake. His proof is correct. Lenny did not make a mistake. His proof is correct. Skip to navigation

Answer 1

Lenny made a mistake when he stated that ∠MLI and ∠MLJ are right angles. According to the definition of a perpendicular bisector, it is angles ∠LMI and ∠LMJ that are right angles, as L is the midpoint of IJ¯¯¯¯¯¯ and HK¯¯¯¯¯¯ is the perpendicular bisector. Therefore, the correct angles to reference in the proof should be ∠LMI and ∠LMJ, not ∠MLI and ∠MLJ. This misrepresentation affects the validity of his reasoning regarding the right angles in relation to the triangles.

Answer 2

So whats the awnser A b C or D

Answer 3

The correct answer is:

C: The definition of a perpendicular bisector tells you that ∠LMI and ∠LMJ are right angles, not that ∠MLI and ∠MLJ are right angles.

This highlights Lenny's mistake concerning the identification of the right angles related to the midpoint and the perpendicular bisector.