For more information on right triangles, see Right Triangles and Pythagorean Theorem. For acute triangles, any of the three sides can act as the base and have a corresponding height. The interior angles at the meeting of the height and base would be 90 o for each new right triangle. The two right triangles resulting from this division would both share the height as one of its sides. Such a line segment would be considered the height or altitude ( h ) for that particular base ( b ). In a triangle, the largest interior angle is opposite to longest side, and vice versa.Īny triangle can be divided into two right triangles by taking the longest side as a base, and extending a line segment from the opposite corner to a point on the base such that it is perpendicular to the base. The triangle as a whole can be labeled by a small triangle symbol and its corner points. The corners or their corresponding angles can be labeled with capital letters. The sides or their lengths of a triangle are typicaly labeled with lower case letters. The side not having this corner as one of its two endpoints can be called the side opposite to the corner. Likewise, if a corner or its angle is chosen, then the two sides sharing an endpoint at that corner can be called adjacent sides. The interior angle whose vertex is the opposite corner can be called the angle opposite to the side. The corner which is not one of these endpoints can be called the corner opposite to the side. If one of the sides of a triangle is chosen, the interior angles of the corners at the side's endpoints can be called adjacent angles. Opposite corners and sides in triangles Picture of Triangle ABC Of course, pairs of triangles which are not equilateral might be similar or congruent.įurther discussion of Congruent Triangles and Similar Triangles may be found in those corresponding sections. However, polygons having four or more equal sides might not have equal interior angles, might not be regular polygons, and might not be similar or congruent. Because the interior angles are all equal, all equilateral triangles are also the three-sided variety of a regular polygon and they are all similar, but might not be congruent. If all three sides of a triangle are of equal length, then it is called an equilateral triangle and all three of the interior angles must be 60 o, making it equiangular. The other two angles are both less than 90 o. In an isosceles triangle, the angle between the two equal sides can be more than, equal to, or less than 90 o. If two of the sides of a triangle are of equal length, then it is called an isosceles triangle. If all three of the sides of a triangle are of different length, then the triangle is called a scalene triangle. Finally, one of the angles can be more than 90 o and the other two less then the triangle is called an obtuse triangle.Ĭategorized by sides One of the angles can be 90 o and the other two less than 90 o then the triangle is called a right triangle. All three angles can all be less than 90 oin the triangle then it is called an acute triangle. This means that no more than one of the angles can be 90 o or more. The sum of the interior angles in a triangle always equals 180 o.
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