| | | GEO0008 -- Orthocenter Theorem |
Theorem. [Orthocenter Theorem] Given a triangle ABC, the three altitudes are concurrent in a point H.
dim 100 100
point A 10 10
point B 50 10
point C 40 70
line a B C
line b A C
line c B A
perp hA A a
perp hB B b
intersec H hA hB
drawsegment A B
drawsegment A C
drawsegment B C
drawline A H
drawline B H
cmark_lt A
cmark_rt B
cmark_lt C
cmark_rt H
drawdashline C H
prove { equal { pythagoras_difference3 A C H } { pythagoras_difference3 B C H } }
| | | GEO0008 -- Orthocenter Theorem |