Question

Please Help asap: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.

Answer 1

The error in this flowchart is:

4. Point L is equidistant from points J and K; Definition of Equidistant.

The flowchart incorrectly states that point L is equidistant from points J and K. However, this is not true. Point L is the midpoint of segment JK, as stated in the correct definition of a perpendicular bisector. The correct statement should be that segment JL is congruent to segment KL, not that point L is equidistant from points J and K.

This error occurs because the flowchart incorrectly connects the congruence of the triangles JNL and KNL (SAS Postulate) to the statement that segment JL is congruent to segment KL. The correct flow should connect the congruence of the triangles to the fact that segment JN is congruent to segment KN (which follows from the definition of a perpendicular bisector). From the congruence of the triangles, we can then conclude that segment JL is congruent to segment KL using the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) postulate.

In summary, the error in the flowchart is that it incorrectly concludes that point L is equidistant from points J and K, when in fact, point L is the midpoint of segment JK.

Answer 2

The error in the flowchart is that an arrow is missing between the given statement and ∠lnk ≅ ∠lnj. To understand this error, let's break down the flowchart and its statements: 1. jl and kl are equal in length, according to the definition of a midpoint. This statement is correct. In a perpendicular bisector, the line segments from the midpoint to the endpoints are equal. 2. point l is equidistant from endpoints j and k, not j and n. This statement is correct as well. A perpendicular bisector is equidistant from the endpoints, not from a different point like n. 3. The arrow between δjnl ≅ δknl and points in the wrong direction. This statement is pointing out an error in the flowchart. The arrow should be reversed to indicate that δjnl ≅ δknl, not the other way around. 4. An arrow is missing between the given statement and ∠lnk ≅ ∠lnj. This statement is also correct. There should be an arrow connecting the given statement (jl and kl are equal in length) with the statement ∠lnk ≅ ∠lnj. This indicates that the equality of the line segments implies the equality of the angles. So, the missing arrow between the given statement and ∠lnk ≅ ∠lnj is the error in the flowchart. This missing arrow prevents the correct conclusion that ∠lnk ≅ ∠lnj can be made based on the given information. To fix the flowchart, we would need to add the missing arrow between the given statement and ∠lnk ≅ ∠lnj, indicating that the equality of the line segments implies the equality of the angles.