Finding the converse of Euclid's fifth postulate (parallel postulate)

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The discussion revolves around finding the converse of Euclid's fifth postulate regarding parallel lines. The original statement asserts that if a line intersects two lines and the interior angles on one side are less than two right angles, the two lines will meet on that side if extended indefinitely. The proposed converse begins with the condition that if two lines meet on a side of a straight line, then the angles on that side are less than two right angles. Participants clarify that the converse follows the logical structure of "if A then B" becoming "if B then A." Understanding this relationship is crucial for mastering geometric principles.
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Homework Statement



I have to state the converse of the following sentence:

That, 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 are the angles less than two right angles.

The Attempt at a Solution



The statement is a mouthful, so I just want to make sure I got the converse right.

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I think you'd do better to begin "If two lines produced indefinitely meet on a side of a straight line that falls upon them then on that side ..."

Are you taking old fashioned geometry?
 
The converse of any statement of the form "if A then B" is "if B then A".
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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