# 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