Question

When the sum of the measures of the interior angles on the same side of the falling line is greater than 180 degree, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is greater than 180 degree.

(a) True

(b) False

The question was posed to me in an interview for internship.

I would like to ask this question from Equivalent Versions of Euclid’s Fifth Postulate topic in portion Euclid’s Geometry of Mathematics – Class 9

Answer 1

Right option is (b) False

Best explanation: The given statement is slightly different from Euclid’s 5^th postulate which is “When the sum of the measures of the interior angles on the same side of the falling line is less than two right angles (<180), then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.”

It can be understood by the diagram given below.

Falling line is PQ and sum of two angles BPQ and YQP is greater than 180 degree and we can see that lines AB and XY will not meet on the right side of the line PQ.