Question

1. given: ∠lkm = ∠jkm, ∠lmk = ∠jmk.

prove: △lkm = △jkm
choose the word that completes the sentence correctly.
proof: ∠lkm = ∠jkm and ∠lmk = ∠jmk are given. overline{km} ≅ overline{km} by the ___ property of congruence.
reflexive
equivalence
symmetric
transitive

Explanation:

The reflexive property of congruence states that any geometric figure is congruent to itself. Here, the segment \( \overline{KM} \) is congruent to itself, which is exactly what the reflexive property describes. The equivalence property is a broader term (including reflexive, symmetric, transitive), but the specific property for a figure being congruent to itself is reflexive. The symmetric property would be if \( A\cong B \) then \( B\cong A \), and the transitive property would be if \( A\cong B \) and \( B\cong C \) then \( A\cong C \). Since we have a single segment \( \overline{KM} \) being congruent to itself, the reflexive property is the correct one.

Answer:

Reflexive