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.

• A. True
• B. False

Answer 1

The correct option is A True

According to Euclid's fifth postulate
If a straight line crossing two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if extended indefinitely, meet on that side on which are the angles less than the two right angles.
Our statement is:
"Two intersecting lines cannot be perpendicular to the same line".
So from the fifth postulate that if two lines meet on third line
As one side on which the sum of angles is less than two right angles
As here two intersecting lines $m$ and $n$ are not perpendicular on line l
$x+y>{180}^{\circ }$
that means lines are not perpendicular to third line as their sum is less than two right angles.
So we can say that given statement is equivalent to Euclid's fifth postulate.