We review how perpendicularity in hyperbolic geometry comes from duality, and then introduce duality for triangles and trilaterals. Then we discuss the orthic triangle and its dual, defining the important Base center point, which lies on the ortho-axis of a triangle, and is also somewhat remarkably the orthocenter of a triangle of orthocenters formed from the bases of the triangle. We introduce a general strategy for approaching theorems in the subject, and introduce our Standard Triangle 1: which will be used to algebraically illustrate many concepts and as an arena for numerical investigations.CONTENT SUMMARY: pg 1: @00:09 Review of basic algebraic framework;?pg 2: @04:38 Dual triangle; triangle, associated trilateral, dual trilateral,associated dual triangle; constructing altitudes to find orthocenterpg 3: @09:30 orthocenter and orthic triangle; dual of orthic triangle; Basecenter theorem @11:46 ; point of perspectivity; base center of trianglepg 4: @13:39 Base ortho-axis theorem; importance of ortho-axispg 5: @15:17 Three steps to understanding theorems; GPS pictures illustrating base center theorem @18:39pg 6: @19:30 standard triangle #1pg? 7: @23:46 computing altitudes with standard triangle #1pg 8: @26:58 computing orthic lines, orthic axis, ortho-axis, base center, using standard triangle #1pg 9: @31:34 Base triple orthocenter theorem; GSP pictures of base triple orthocenter theorem @33:02 pg 10: @33:28 more (st#1) base triple orthocenter (THANKS to EmptySpaceEnterprise)
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