How do you find the orthocenter of a triangle?


Quick Answer

You can locate the orthocenter of a triangle by drawing the altitudes of each of the triangle's sides and pinpointing the point at which all three lines intersect. The triangle must be an acute triangle for it to have its orthocenter inside the triangle.

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How do you find the orthocenter of a triangle?
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Full Answer

  1. Identify the type of triangle

    Verify the triangle does not have angles greater than or equal to 90 degrees to ensure it's an acute triangle. Only acute triangles have orthocenters in the interior. A right triangle has its orthocenter at the vertex of its right angle.

  2. Draw the altitude perpendicular to the base

    Draw a straight line from the triangle's top vertex down to the base. Ensure that this line creates a right angle with the base. This is one of the triangle's altitudes.

  3. Draw the other altitudes of the triangle

    Obtain the altitude for the two other sides by using the same method. Rotate the triangle so that the new side is nearest to you, and then draw the altitude from the vertex opposite it. Make sure that each altitude forms a right angle with the side to which it is connected.

  4. Find the point of intersection

    The orthocenter is where the three altitudes intersect into one point. Locate this point, and label it "O" for orthocenter.

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