Question

question 14 (multiple choice worth 1 points)
(03.06r.mc)
which statement is not used to prove that δlkm is similar to δnom?
angle k is congruent to itself, due to the reflexive property
angles mon and mkl are congruent, due to the corresponding angles postulate
km is a transversal intersecting lkand on
segments kl and on are parallel

Explanation:

Step1: Recall the AA (Angle - Angle) similarity criterion

For two triangles \(\triangle LKM\) and \(\triangle NOM\) to be similar, we need two pairs of congruent angles. If \(KL\parallel ON\) (given by the statement "Segments \(KL\) and \(ON\) are parallel"), and \(KM\) is a transversal (given by the statement "\(KM\) is a transversal intersecting \(LK\) and \(ON\)"), then \(\angle LKM=\angle NOM\) (corresponding angles postulate, given by the statement "Angles \(MON\) and \(MKL\) are congruent, due to the corresponding angles postulate") and \(\angle LMK=\angle NMO\) (common angle).

Step2: Analyze the role of each statement

• The statement "Angle \(K\) is congruent to itself, due to the reflexive property" is not relevant. In \(\triangle LKM\) and \(\triangle NOM\), the common angle is \(\angle M\) (not \(\angle K\)). The reflexive property (\(\angle A=\angle A\)) is used when we have a single - triangle context for congruence (like in \(SAS\) congruence of a triangle with itself) or in some special similarity cases where an angle is shared in a non - parallel line - transversal setup. Here, since we have parallel lines \(KL\parallel ON\) and transversal \(KM\), the key angles for similarity (\(\angle LKM\) and \(\angle NOM\), \(\angle LMK\) and \(\angle NMO\)) do not involve using the reflexive property for \(\angle K\).

Answer:

Angle \(K\) is congruent to itself, due to the reflexive property.