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    Altitude of a Triangle

    Illustration

    Illustration

    Basic definition

    An altitude of a triangle is a line segment from one of its vertices which meets the opposite side at a right angle.

    Detailed definition

    The altitudes of a triangle are the Cevians A_i H_i that are perpendicular to the legs A_j A_k opposite A_i. The three altitudes of any triangle are concurrent at the orthocenter H. This fundamental fact did not appear anywhere in Euclid's Elements. The triangle Δ H_1 H_2 H_3 connecting the feet of the altitudes is known as the orthic triangle.

    Related terms

    Cevian | maltitude | orthic triangle | orthocenter | perpendicular | perpendicular foot | Taylor circle

    Educational grade level

    middle school level (California grade 7 standard)

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