Question

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? A.) JL and KL are equal in length, according to the definition of a midpoint. B.) The arrow between ΔJNL ≅ ΔKNL and segment JL is congruent to segment KL points in the wrong direction. C.) Segments JL and KL need to be constructed using a straightedge. D.) Point L is equidistant from points J and N, not J and K.

Answer 1

Choice D is not the correct answer. Point L is equally distant from J and K. In other words, JL = LK. If two friends lived at points J and K, then point L would be a good meeting spot as they would travel the same distance. Point N has the same properties as point L does (with regard to being equally distant from J and K). It is not correct to say that LJ = JN.

The answer is actually choice C. Segments JL and KL need to be constructed using a straightedge.

Otherwise, these segments are not going to be shown and you cannot use them. A segment is simply a straight line between two endpoints. Two triangles form (triangle JNL and KNL) to help with the proof, so it's very beneficial to draw in these segments. It might help to use a different color pen, or lightly draw the segment using a faint pencil mark to erase later.