Question

For every line l and for every point p not lying on l, how many unique line m passes through p and parallel to l ?

• A. Two
• B. Three
• C. Only one
• D. Four

Answer 1

The correct option is C Only one

According to the fifth postulate of Euclid, the intersection of lines will take place where sum of measures of interior angles on the same side of the line is less than ${180}^0$.
One of the equivalent versions of this postulate is ‘Playfair's axiom’, which states that for every line and for every point not lying on the line, there exists a unique line passing through that point and parallel to the given line.
Thus, the statement only one unique line m passes through p and parallel to l.

Hence, the correct answer is option (c).