Geometry/Neutral Geometry/Pasch and Crossbar

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Pasch's Theorem[edit | edit source]

If A, B, C are distinct noncollinear points and l is any line intersecting AB in a point between A and B, then l also intersectseither AC or BC. If C does not lie on l, then l does not intersect both AC and BC

Explanation[edit | edit source]

Crossbar Theorem[edit | edit source]

If ray AD (need LaTex formatting) is between ray AC(need LaTex formatting) and ray AB(need LaTex formatting), then ray AD(need LaTex formatting) intersects segment BC

Explanation[edit | edit source]