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The easiest, most straightforward way to calculate the orthocenter of a triangle is to follow this step-by-step guide: To start, let's assume that the triangle ABC has the vertex coordinates A = (x₁, y₁), B = (x₂, y₂), and C = (x₃, y₃). Find the slope of one side of the triangle, e.g., AB.
The orthocenter of a triangle is the point of intersection of any two of three altitudes of a triangle (the third altitude must intersect at the same spot). You can find where two altitudes of a triangle intersect using these four steps:
The orthocenter of a triangle is the point where the perpendicular drawn from the vertices to the opposite sides of the triangle intersect each other. For an acute angle triangle, the orthocenter lies inside the triangle. For the obtuse angle triangle, the orthocenter lies outside the triangle.
Define the orthocenter and learn how to find the orthocenter of a triangle in four steps with this free geometry video. Follow along using the transcript.
Orthocenter of a triangle is the point of intersection where all three altitudes of a triangle meet. Learn more about the orthocenter of a triangle, its properties, formula along with solving a few examples.
The orthocenter of a triangle is the intersection of the triangle's three altitudes. It has several important properties and relations with other parts of the triangle, including its circumcenter, incenter, area, and more.
How to construct the orthocenter of a triangle with compass and straightedge or ruler. The orthocenter is the point where all three altitudes of the triangle intersect. An altitude is a line which passes through a vertex of the triangle and is perpendicular to the opposite side.
The orthocenter of a triangle can be found using two main methods. We can sketch the heights of the triangle and find the point of intersection. Alternatively, we can find the coordinates of the orthocenter algebraically.
It turns out that all three altitudes always intersect at the same point - the so-called orthocenter of the triangle. 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.
Examples, solutions, videos, worksheets, games, and activities to help Geometry students learn how to construct the orthocenter of a triangle. The following diagrams show the orthocenters of different triangles: acute, right, and obtuse.