![]() ![]() This says the product of the hypotenuse and the altitude of a right triangle (in this case, ) is equal to the product of its legs. If we consider the hypotenuse and short leg of each, the following ratios of corresponding parts are equal. Notice that d + e = c.Īs an example, consider. In, the length of the hypotenuse is a and the length of is h let e be the length of. ![]() Then in, b is the length of the hypotenuse let d be the length of and h the length of, which is the altitude of. These similarities lead to important proportions, which can be more easily represented if we label the sides of the triangles: In, let a be the length of the side opposite angle A, b be the length of the side opposite angle B, and c be the length of the hypotenuse. In the above, the letters are in the order of double-marked angle, right angle, single-marked angle. Notice that the similarities must be named consistently. The altitude to the hypotenuse forms three similar triangles: Triangle ABC is a right triangle with hypotenuse and altitude : In the special case of a right triangle, each leg is an altitude perpendicular to the other leg, and there is a third altitude from the right angle perpendicular to the hypotenuse that plays an important role in measurement The dashed segments,, in the following figures are altitudes of the triangles: An altitude of any triangle is a segment that extends from a vertex to the opposite side (or an extension of the opposite side) and is perpendicular to that side. ![]()
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