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{{ printedBook.courseTrack.name }} {{ printedBook.name }} We are given information about lines in a plane.

- Line $a$ is parallel to line $b.$
- Line $b$ is parallel to line $c.$
- Line $d$ is perpendicular to line $a.$

We are given statements and asked which of them that **must** be true. Let's draw a diagram to illustrate the situation.

Since line $d$ intersects lines $a,$ $b,$ and $c,$ it is **not** parallel to any of them. Therefore, neither statement **I,** nor **II** can be true true. To determine whether statement **III** is true, we will use the following theorem.
$\begin{gathered}
\textit{If two lines are parallel to the same line,}\\
\textit{then they are parallel to each other.}\\[0.8em]
\end{gathered}$
In our case, lines $a$ and $c$ are both parallel to $b.$ Therefore, according to the above theorem, lines $a$ and $c$ are parallel.
$\begin{gathered}
a \text{ and } b \text{ are parallel } \\ \text{ and } \\ b \text{ and } c \text{ are parallel } \\ \Downarrow \\ a \text{ and } c \text{ are parallel }
\end{gathered}$
If two lines are parallel they can not be perpendicular. Thus, statement **III** is the one that must be true.