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What is the definition of the "altitude of a triangle"?

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Quick Answer

The altitude of a triangle is defined as the line drawn from the vertex of a triangle and perpendicular to the opposite side of the triangle. A triangle has three sides and three vertices. Hence, it has three altitudes.

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Full Answer

Altitudes may also lie outside a triangle. In a triangle with all three acute angles, all altitudes lie within the triangle. For an obtuse angled triangle, one or more altitudes may lie outside the triangle.

The altitudes of a triangle are useful when calculating the area of the triangle. The area of a triangle is half the product of its base and the corresponding altitude.

All three altitudes of a triangle intersect at a point called the orthocenter. The orthocenter may lie inside or outside the triangle.

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