iran-konkur 2017 Q131

iran-konkur · Other · konkur-riazi_1396_specialized Not Maths
131. Which converse of the following statements holds in space?
  1. [(1)] If two lines $d$ and $d'$ are parallel, then every line perpendicular to $d$ is perpendicular to $d'$.
  2. [(2)] If a line is parallel to one of the planes, then the line is parallel to that plane.
  3. [(3)] If two planes $P$ and $Q$ are parallel, then the intersection lines of plane $R$ with them are parallel to each other.
  4. [(4)] If two planes $P$ and $Q$ are parallel, then they create proportional segments on two intersecting lines.

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\textbf{131.} Which converse of the following statements holds in space?

\begin{enumerate}
    \item[(1)] If two lines $d$ and $d'$ are parallel, then every line perpendicular to $d$ is perpendicular to $d'$.
    \item[(2)] If a line is parallel to one of the planes, then the line is parallel to that plane.
    \item[(3)] If two planes $P$ and $Q$ are parallel, then the intersection lines of plane $R$ with them are parallel to each other.
    \item[(4)] If two planes $P$ and $Q$ are parallel, then they create proportional segments on two intersecting lines.
\end{enumerate}



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