The following is an incorrect flowchart proving that point L, lying on line LM which is a perpendicular bisector of segment JK, is equidistant from points J and K:
Segment JK intersects line LM at point N.
Line LM is a perpendicular bisector of segment JK; Given. Two arrows are drawn from this statement to the following two statements. Segment JN is congruent to segment NK; Definition of a Perpendicular Bisector. Angle LNK equals 90 degrees, and angle LNJ equals 90 degrees; Definition of a Perpendicular Bisector. An arrow is drawn from this last statement to angle LNK is congruent to angle LNJ; Definition of Congruence. Segment LN is congruent to segment LN; Reflexive Property of Equality. Three arrows from the previous three statements are drawn to the statement triangle JNL is congruent to triangle KNL; Side Angle Side, SAS, Postulate. An arrow from this statement is drawn to the statement segment JL is congruent to segment KL; Corresponding Parts of Congruent Triangles are Congruent CPCTC. An arrow from this statement is drawn to JL equals KL; Definition of Congruence. An arrow from this statement is drawn to Point L is equidistant from points J and K; Definition of Equidistant.
What is the error in this flowchart?
JL and KL are equal in length, according to the definition of a midpoint.
The arrow between ΔJNL ≅ ΔKNL and segment JL is congruent to segment KL points in the wrong direction.
Segments JL and KL need to be constructed using a straightedge.
Point L is equidistant from points J and N, not J and K.
