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  • 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.

Study the following statement: “Two intersecting lines cannot be perpendicular to the same line”. Check whether it is an equivalent version to Euclid’s fifth postulate.

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Euclid’s fifth postulate: if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines if produced indefinitely, meet on that side on which the angles are less than two right angles.

It means that if the sum of angles \angleA and \angleB in the figure is less than the sum of two right angles then A, and B meet on the same side of angles A and B continue indefinitely.

Now the given statement is “Two intersecting lines cannot be perpendicular to the same line”

Hence we can see that the lines A1 and B1 are intersecting and so, are not perpendicular to the same line (D).

The given statement “Two intersecting lines cannot be perpendicular to the same line” is an equivalent version of Euclid’s fifth postulate. Because it is a conclusion from the fifth postulate.  

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