Answer
Only one line can be drawn through a given point which is parallel to a given line if a line is given and a point is not given on the line.
Work Step by Step
Draw a\[\vartriangle ABC\], where l line is drawn through given point A and is parallel to given line m.
Since the lines are parallel, the alternate interior angles will be equal.
Therefore, m\[\measuredangle 4=\text{m}\measuredangle 2\] and\[m\measuredangle 5=\text{m}\measuredangle 3\]. Observe that angles 4, 1 and 5 form a straight angle. Therefore, their sum will be equal to\[{{180}^{\circ }}\].
\[\measuredangle 4+\measuredangle 1+\measuredangle 5=180{}^\circ \]
As m\[\measuredangle 4=\text{m}\measuredangle 2\] and m\[\measuredangle 5=\text{m}\measuredangle 3\], substitute \[\measuredangle 4\] with \[\measuredangle 2\]and \[\measuredangle 5\]with\[\measuredangle 3\]. Therefore,\[\measuredangle 2+\measuredangle 1+\measuredangle 3=180{}^\circ \].
This equation shows that the sum of measurement of three angles of a triangle is\[180{}^\circ \].
Hence, only one line can be drawn through a given point which is parallel to a given line if a line is given and a point is not given on the line.
