The Orthocenter of a Triangle | Definition, Construction, and Properties

Orthocenter

The orthocenter is a point of intersection in a triangle where the three altitudes of the triangle meet

The orthocenter is a point of intersection in a triangle where the three altitudes of the triangle meet. An altitude is a line segment drawn from a vertex of the triangle perpendicular to the opposite side. The orthocenter is not always located within the triangle; it can also be outside the triangle.

To find the orthocenter of a triangle, you need to locate the intersection point of the three altitudes. Here are the steps to find the orthocenter:

1. Draw a triangle and label its vertices as A, B, and C.

2. Draw a line segment from vertex A perpendicular to side BC. The point where this line intersects side BC is called the foot of the altitude from vertex A, denoted as D.

3. Repeat step 2 for the other two vertices. Draw a line segment from vertex B perpendicular to side AC, intersecting AC at E. Draw another line segment from vertex C perpendicular to side AB, intersecting AB at F.

4. Connect the points D, E, and F. The intersection of these lines is the orthocenter of the triangle.

It’s important to note that not all triangles have a unique orthocenter. In an acute triangle, where all angles are less than 90 degrees, the orthocenter lies inside the triangle. In an obtuse triangle, where one angle is greater than 90 degrees, the orthocenter will be outside the triangle. In a right triangle, where one angle is exactly 90 degrees, the orthocenter will coincide with one of the vertices.

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