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.]

Question

Philoid · Accepted Answer

Two equivalent version of Euclid’s fifth postulate are:

• For every line L and for every point P not lying on the L, there exists a unique line M passing through P and parallel to L.

• Two distinct intersecting lines cannot be parallel to the same line.

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

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.]

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.]