The right triangle is the in-between case: both its circumcenter and its orthocenter lie on its boundary. Likewise, a triangle's circumcenter-the intersection of the three sides' perpendicular bisectors, which is the center of the circle that passes through all three vertices-falls inside an acute triangle but outside an obtuse triangle. These altitudesįall entirely outside the triangle, resulting in their intersection with each other (and hence with the extended altitude from the obtuse-angled vertex) occurring in the triangle's exterior. But for an obtuse triangle, the altitudes from the two acute angles intersect only the extensions of the opposite sides.
In the case of an acute triangle, all three of these segments lie entirely in the triangle's interior, and so they intersect in the interior. The orthocenter is the intersection point of the triangle's three altitudes, each of which perpendicularly connects a side to the opposite vertex. However, while the orthocenter and the circumcenter are in an acute triangle's interior, they are exterior to an obtuse triangle. In all triangles, the centroid-the intersection of the medians, each of which connects a vertex with the midpoint of the opposite side-and the incenter-the center of the circle that is internally tangent to all three sides-are in the interior of the triangle. Regardless, to draw any altitude of triangle, you need the triangle in question, and a method of drawing or detecting a particular angular measure. Since a triangle's angles must sum to 180° in Euclidean geometry, no Euclidean triangle can have more than one obtuse angle.Īcute and obtuse triangles are the two different types of oblique triangles - triangles that are not right triangles because they have no 90° angle. Answer (1 of 1): Any obtuse triangle will necessarily have two angles that are not obtuse (assuming Euclidean geometry). An obtuse triangle (or obtuse-angled triangle) is a triangle with one obtuse angle (greater than 90°) and two acute angles.
An acute triangle (or acute-angled triangle) is a triangle with three acute angles (less than 90°).
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