Let's have a look at the diagram, including the given information that MN≅ LQ and LQ≅ PN.
According to the diagram, MN≅ PN. This is in fact true but not by the Reflexive Property of Segment Congruence. This property tells us that a segment is congruent to itself. However, the property used to make the congruence statement is the Transitive Property of Segment Congruence.
MN≅ LQ, LQ≅ PN
⇓
MN≅ PN
Let's change the statement.
Because MN≅ LQ and LQ≅ PN, then MN≅ PN by the Transitive Property of Segment Congruence (Theorem 2.1).
