5.5 The Fifth Postulate: The Complexity of Parallels

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Step 1

Postulate 5 states that if the sum of interior angles is less than 180 degrees, lines meet.

Step 2

This logically implies the boundary condition: If the sum equals 180 degrees, they do not meet.

Step 3

Lines that do not meet are defined as parallel lines. Thus, the postulate implicitly defines the condition for parallelism.

Final Answer

Yes, by defining the condition for non-intersection.

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