The orthocenter is the point of concurrency of the altitudes in a triangle.
A point of concurrency is the intersection of 3 or more lines, rays, segments or planes.
The orthocenter is just one point of concurrency in a triangle.
The others are the incenter, thecircumcenter and the centroid.
The orthocenter is not always inside the triangle. If the triangle is obtuse, it will be outside. To make this happen the altitude lines have to be extended so they cross. Adjust the figure above and create a triangle where the orthocenter is outside the triangle. Follow each line and convince yourself that the three altitudes, when extended the right way, do in fact intersect at the orthocenter.
Video: “Constructing the Orthocenter of a Triangle"
The ortho-center,centroid and and circum-circle are some different concepts related to triangle and its geometry.
ReplyDeleteBut these are very helpful in understanding real life calculations.
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