An arrow is missing between angle LNK 90 and angle LNJ 90 an...

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### Correct Answer An arrow is missing between \( \angle LNK = 90^\circ \) and \( \angle LNJ = 90^\circ \) and \( \angle LNK \cong \angle LNJ \). ### Step-by-Step Explanation 1. **Understand the Perpendicular Bisector Definition**: A perpendicular bisector of a segment is a line that is perpendicular to the segment (forming \( 90^\circ \) angles) and bisects it (divides it into two equal parts). For \( \overleftrightarrow{LM} \) (the perpendicular bisector of \( \overline{JK} \)): - \( \angle LNK = 90^\circ \) and \( \angle LNJ = 90^\circ \) (by the *definition of a perpendicular bisector*). 2. **Analyze Angle Congruence**: If two angles are both \( 90^\circ \), they are congruent (all right angles are congruent). In the flowchart, the step \( \angle LNK = 90^\circ \) and \( \angle LNJ = 90^\circ \) should logically lead to \( \angle LNK \cong \angle LNJ \), but the arrow connecting these statements is missing. ### Relevant Knowledge Points - **Perpendicular Bisector**: A line that is perpendicular to a segment (forms \( 90^\circ \) angles with it) and divides the segment into two congruent parts. - **Right Angles and Congruence**: All right angles (\( 90^\circ \) angles) are congruent. - **Flowchart Proof Structure**: Each step in a proof flowchart should have a logical connection (arrow) to the next step, showing how conclusions follow from previous statements. ### Explanation of Relevant Knowledge Points - **Perpendicular Bisector Definition**: If a line is a perpendicular bisector of a segment, it intersects the segment at its midpoint and forms right angles with the segment. Thus, \( \overleftrightarrow{LM} \perp \overline{JK} \) implies \( \angle LNK = \angle LNJ = 90^\circ \). - **Right Angle Congruence**: Angles with the same measure (e.g., two \( 90^\circ \) angles) are congruent. So \( \angle LNK \cong \angle LNJ \) because both are \( 90^\circ \). - **Flowchart Logic**: In a proof flowchart, every conclusion (e.g., \( \angle LNK \cong \angle LNJ \)) must be linked (via an arrow) to the statement(s) that justify it (e.g., \( \angle LNK = 90^\circ \) and \( \angle LNJ = 90^\circ \)). The missing arrow here breaks the logical flow of the proof. By identifying the missing logical connection (arrow) between the right angle measures and their congruence, we determine the error in the flowchart.

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