The altitude of a triangle IS a geometric concept so it intersects geometry in its very existence.
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The orthocenter of a triangle may lie outside the triangle because an altitude does not necessarily intersect the sides of the triangle.
Well, isn't that a happy little question! The altitude of a triangle is always perpendicular to the base it intersects. It's like a little friend that helps the triangle stand tall and proud. Just remember, in the world of triangles, altitudes are always there to lend a hand and make everything more balanced and beautiful.
In geometry, a perpendicular segment that connects a vertex to its opposite side is the altitude of a triangle. Triangles have three altitudes, according to this definition for altitude.
A right triangle in geometry is a triangle that has 90 degrees as one of its angles.
It depends on how you define "ways" and how you define "lines" and how you define "intersect" and what kind of geometry you're talking about, but in Euclidean geometry, lines either never intersect, or they intersect at a single point, or they can intersect at all points within the lines.