Obtuse: The altitude connected to the obtuse vertex is inside the triangle, and the two altitudes connected to the acute vertices are outside the triangle. The altitude can be inside the triangle, outside it, or even coincide with one of its sides, it depends on the type of triangle it is: Obtuse triangle: The altitude related to the longest side is inside the triangle (see h c, in the triangle above) the other two heights are outside the triangle (h a, and h b). Right: The altitude perpendicular to the hypotenuse is inside the triangle the other two altitudes are the legs of the triangle (remember this when figuring the area of a right triangle). Isosceles: Two altitudes have the same length.Įquilateral: All three altitudes have the same length.Īcute: All three altitudes are inside the triangle. ![]() Scalene: None of the altitudes has the same length. The following points tell you about the length and location of the altitudes of the different types of triangles: We see that the orthocentre may lie within, on or outside the triangle. In an obtuse-angled ∆XYZ, the altitudes with respect to XY, YZ, and ZX are ZR, XP, and YQ respectively. Thus, the three altitudes XY, YZ, and YM intersect at Y. Here we see that XY ⊥ YZ, YZ ⊥ XY, and YM ⊥ XZ. In the adjoining figure ∆XYZ is a right-angled triangle. In the adjoining figure, the three altitudes XP, YQ, and ZR intersect at the orthocentre O. The point at which they intersect is known as the orthocentre of the triangle. ![]() The three altitudes of a triangle are concurrent. Formally, the shortest line segment between a vertex of a triangle and the (possibly extended) opposite side. The distance between a vertex of a triangle and the opposite side is an altitude. ![]() The intersection of the extended base and the altitude is called the foot of the altitude. This line containing the opposite side is called the extended base of the altitude. Sometimes the opposite side isn’t quite long enough to draw an altitude, so we are allowed to extend it to make an altitude possible.
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