Orthocenter
Orthocenter
Load Eos
Load Eos
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<<EosLoader`
Eos3.7.1.1 (March 21,2023) running under Mathematica 13.2.0 for Mac OS X ARM (64-bit) (November 18, 2022) on Thu 30 Mar 2023 14:43:35.
Orthocenter
Orthocenter
The three (possibly extended) altitudes intersect in a single point H of the triangle. Point H is called the orthocenter of the triangle.
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EosSession["Orthocenter"];
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MarkOff[];
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NewOrigami[10]
Orthocenter: Step 1
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NewPoint["E"{6,7}]
Orthocenter: Step 1
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HO["AE"]!
Orthocenter: Step 3
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HO["BE"]!
Orthocenter: Step 5
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HO["AE","B",Mark{"AE"}]!
Orthocenter: Step 7
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HO["BE","A",Mark{{"EB"}}]!
Orthocenter: Step 9
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HO["AB","E",Mark{{"AB","I"},{"AG","H"}}]!
Orthocenter: Step 11
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triangle={Thick,Red,Line[{"A","B","E","A"}]};
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ShowOrigami[More{triangle}]
Orthocenter: Step 11
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Goal[CollinearQ["A","H","G"]∧CollinearQ["B","H","F"]];
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Prove["Orthocenter",Mapping{"A"{0,0},"B"{1,0},"C"{1,1},"D"{0,1},"E"{u,v}}]
Proof is successful.
Orthocenter: Step 11
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EndSession[];