Easy
Write whether the following statement is True or False. Justify your answer.
Two distinct intersecting lines cannot be parallel to the same line.
Two distinct intersecting lines cannot be parallel to the same line.
(A) The statement is $True$.
Justification: According to Playfair's Axiom,which is an equivalent version of Euclid's fifth postulate,if a line $l$ and a point $P$ (not on $l$) are given,there exists exactly one line $m$ passing through $P$ such that $m$ is parallel to $l$.
If two distinct intersecting lines $m_1$ and $m_2$ were both parallel to the same line $l$,it would contradict the property that through a point not on a given line,there is only one unique line parallel to the given line. Therefore,two distinct intersecting lines cannot be parallel to the same line.
Justification: According to Playfair's Axiom,which is an equivalent version of Euclid's fifth postulate,if a line $l$ and a point $P$ (not on $l$) are given,there exists exactly one line $m$ passing through $P$ such that $m$ is parallel to $l$.
If two distinct intersecting lines $m_1$ and $m_2$ were both parallel to the same line $l$,it would contradict the property that through a point not on a given line,there is only one unique line parallel to the given line. Therefore,two distinct intersecting lines cannot be parallel to the same line.
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