Ruler and Compass Construction 18B
Altitudes of a Triangle Meeting at Orthocenter

1. Perpendicular from C to AB (construction 1)
2. Altitude CG
3. Perpendicular from A to BC
4. Altitude AM
5. Altitudes intersect at orthocenter N
6. Ray BN
7. Third altitude BP
Why it works: An altitude is a segment from a vertex perpendicular to the opposite side, so the construction of a perpendicular from a point to a line is used twice. It is a theorem that the three altitudes are concurrent, so the third altitude can simply be drawn through the intersection of the first two.
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