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Q.

'Two intersecting lines cannot be parallel to the same line' is stated in which of the following forms?

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a

 An axiom

b

 A definition

c

 A converse

d

 A theorem

answer is A.

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Detailed Solution

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The statement "Two intersecting lines cannot be parallel to the same line" is a fundamental principle in Euclidean geometry, and is therefore an axiom. Axioms are statements or propositions that are assumed to be true without proof and form the basis for a mathematical theory or system.

For example, consider the three lines P, Q, and R shown below:

Question Image

The lines P and Q intersect in the figure above, and line R is parallel to line Q, but nonparallel to line P. Intersecting lines are never parallel to each other. 

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