Exercise 33 Page 475

Let's have a look at the diagram, including the given information that $\overline{MN}\cong \overline{LQ}$ and $\overline{LQ}\cong \overline{PN}.$

According to the diagram, $\overline{MN}\cong \overline{PN}.$ 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. Let's change the statement.

Because $\overline{MN}\cong \overline{LQ}$ and $\overline{LQ}\cong \overline{PN},$ then $\overline{MN}\cong \overline{PN}$ by the Transitive Property of Segment Congruence (Theorem $2.1$).