Question

Which statement is not used to prove that δlkm is similar to δnom? triangles lkm and nom in which point o is between points k and m and point n is between points l and m 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 lk and on. segments kl and on are parallel.

Answer 1

To determine which statement is not used to prove the similarity of the triangles, we need to evaluate each statement in relation to the given information about the triangles.

Step-by-step explanation:

In order to determine which statement is not used to prove that Δlkm is similar to Δnom, we need to evaluate each statement in relation to the given information about the triangles.

1. Angle k is congruent to itself due to the reflexive property. This statement is correct and can be used to prove the triangles are similar.
2. Angles mon and mkl are congruent due to the corresponding angles postulate. This statement is also correct and can be used to prove the triangles are similar.
3. KM is a transversal intersecting LK and ON. This statement is incorrect and cannot be used to prove the triangles are similar.
4. Segments KL and ON are parallel. This statement is correct and can be used to prove the triangles are similar.

Therefore, the statement that is not used to prove that Δlkm is similar to Δnom is that KM is a transversal intersecting LK and ON.

Answer 2

The statement that is not used to prove similarity is: Segments KL and ON are parallel.

To demonstrate that lkm is identical to nom, we must show that all matching angles and sides are congruent and proportional.

Because of the reflexive characteristic, Angle K is congruent to itself. This creates one congruent pair of related angles.

Because of the comparable angles postulate, angles MON and MKL are congruent. This creates a new pair of congruent matching angles.

LK and ON are parallel segments. This statement does not establish similarity between lkm and nom; rather, it establishes parallelism between segments.