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 stateme what is the error in this flowchart? (5 points) jl and kl are equal in length, according to the definition of a midpoint. an arrow is missing between ∠lnk = 90° and ∠lnj = 90° and ∠lnk ≅ ∠lnj. an arrow is missing between the given statement and ∠lnk ≅ ∠lnj. triangles jnl and knl are congruent by the angle-angle side (aas) postulate.

Answer 1

The error in the flowchart lies in the missing arrow between the given statement and the conclusion that ∠lnk ≅ ∠lnj.

Step-by-step explanation:

The flowchart attempts to demonstrate that point l, lying on the perpendicular bisector line lm of segment jk, is equidistant from points j and k. The given information includes the fact that line lm is a perpendicular bisector of segment jk. However, the flowchart overlooks the essential connection between this statement and the conclusion that ∠lnk ≅ ∠lnj.

The missing arrow is critical as it fails to explicitly link the perpendicular bisector property with the congruence of the angles ∠lnk and ∠lnj. The congruence of these angles is crucial for establishing the equidistance of point l from points j and k. Without this connection, the flowchart lacks a proper justification for the equidistance claim.

It's important to note that while the flowchart correctly identifies the midpoint property (jl and kl are equal in length) and the right angles (∠lnk = 90° and ∠lnj = 90°), the logical link between the perpendicular bisector property and the congruence of angles is the missing piece for a comprehensive and valid proof. Therefore, adding an arrow between the given statement and the congruence of angles is necessary to rectify the error and strengthen the flowchart's validity.

Answer 2

The flowchart inaccurately states that point L is equidistant from end points J and K, not adhering to geometric principles. Other errors include the misdirection of an arrow and the absence of a connection between given information and angle congruence.

The flaw in the flowchart becomes evident when scrutinizing option B. The flowchart asserts that point L is equidistant from end points J and K, which is inaccurate. In geometry, the midpoint of a line segment is equidistant from its two endpoints. However, the flowchart contradicts this principle, incorrectly claiming that point L is equidistant from J and K.

Moreover, the arrow connecting the statement ∆JNL ≅ ∆KNL and the conclusion JL ≅ KL points in the wrong direction. The arrow implies that the congruence of the triangles leads to the equality of line segments JL and KL, which is an incorrect interpretation of the congruence statement.

Additionally, there is a missing arrow between the given statement and the conclusion ∠LNK ≅ ∠LNJ. The absence of this arrow disrupts the logical flow of the proof, as it fails to connect the given information about the triangles with the congruence of the corresponding angles.

In summary, the primary error in the flowchart is the misstatement that point L is equidistant from end points J and K, when, according to geometric principles, it should be equidistant from the endpoints of the line segment JK. The misdirection of the arrow and the missing connection between given information and angle congruence further contribute to the inaccuracies in the flowchart.