Question

Study the following statement:

“Two intersecting lines cannot be perpendicular to the same line”.

Check whether it is an equivalent version to the Euclid’s fifth postulate.

[Hint: Identify the two intersecting lines l and m and the line n in the above statement.]

Answer 1

Two equivalent versions of Euclid’s fifth postulate are as follows:

1. For every line l and for every point P not lying on l, there exists a unique line m passing through P and parallel to l.
2. Two distinct intersecting lines cannot be parallel to the same line.

From above two statements it is clear that given statement is not an equivalent version to the Euclid’s fifth postulate.