Mathematics Questions and Answers – Equivalent Versions of Euclid’s Fifth Postulate

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Equivalent Versions of Euclid’s Fifth Postulate”.

1. 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
View Answer

Answer: b
Explanation: The given statement is slightly different from Euclid’s 5th 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.
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2. “For every line x and for every point o not lying on x, there exists a unique line y passing through o and parallel to x.” This statement is __________
a) Pythagoras’ theorem
b) Heron’s theorem
c) Thales’ theorem
d) Playfair’s axiom
View Answer

Answer: d
Explanation: The given statement is Playfair’s axiom which is in fact, equivalent version of Euclid’s fifth postulate.
It can be understood by seeing the diagram given below.

We can see that lines x and y are parallel, i.e. they will not intersect each other.

Sanfoundry Global Education & Learning Series – Mathematics – Class 9.

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Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter