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Common Perp Thm - through P Proof Let l be any line and let...

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The "Common Perpendicular" Theorem In the axiom system being developed, the "Common Perpendicular" Theorem follows the "Drop a Perpendicular" Theorem immediately. Theorem (NIB), The "Common Perpendicular" Theorem: Given any line l and any point P not on line l , there exists a line m passing through P such that l and m share a common perpendicular line that also passes
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Unformatted text preview: through P. Proof: Let l be any line and let P be a point not on line l . By the "Drop a Perpendicular" Theorem, there is a unique line t such that t passes through P and l ⊥ t . By the "Drop a Perpendicular" Theorem, there is unique line m such that m passes through P and t ⊥ m . Therefore, l and m share the common perpendicular t . Q E D P l t P l m t P l...
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