Acute and obtuse triangles Acute and obtuse triangles An acute triangle is a triangle with all three angles acute (less than 90°). An obtuse triangle is one with one obtuse angle (greater than 90°) and two acute angles. Since a triangle's angles must sum to 180°, no triangle can have more than one obtuse angle. Acute and obtuse triangles are the two different types of oblique triangles—triangles that are not right triangles because they have no 90° angle. 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
Triangle it; this is the exterior angle theorem. The sum of the measures of the three exterior angles (one for each vertex) of any triangle is 360 degrees. Two triangles are said to be "similar" if every angle of one triangle has the same measure as the corresponding angle in the other triangle. The corresponding sides of similar triangles have lengths that are in the same proportion, and this property is also sufficient to establish similarity. Some basic theorems about similar triangles are: Two triangles that are congruent have exactly the same size and shape: all pairs of corresponding interior angles