![]() An exterior angle of a triangle is an angle that is a linear pair (and hence supplementary) to an interior angle. This allows determination of the measure of the third angle of any triangle, given the measure of two angles. This fact is equivalent to Euclid's parallel postulate. The sum of the measures of the interior angles of a triangle in Euclidean space is always 180 degrees. The measures of the interior angles of the triangle always add up to 180 degrees (same color to point out they are equal). It follows that in a triangle where all angles have the same measure, all three sides have the same length, and therefore is equilateral. A right degenerate triangle has collinear vertices, two of which are coincident.Ī triangle that has two angles with the same measure also has two sides with the same length, and therefore it is an isosceles triangle. A triangle with an interior angle of 180° (and collinear vertices) is degenerate.If c is the length of the longest side, then a 2 + b 2 < c 2, where a and b are the lengths of the other sides. A triangle with one interior angle measuring more than 90° is an obtuse triangle or obtuse-angled triangle.If c is the length of the longest side, then a 2 + b 2 > c 2, where a and b are the lengths of the other sides. A triangle with all interior angles measuring less than 90° is an acute triangle or acute-angled triangle.Triangles that do not have an angle measuring 90° are called oblique triangles.Right triangles are fundamental in trigonometry, as they can be used to define trigonometric functions through trigonometric ratios. The other one is an isosceles triangle that has 2 angles measuring 45 degrees (45–45–90 triangle). In this situation, 3, 4, and 5 are a Pythagorean triple. The 3–4–5 triangle is also known as the Egyptian triangle. One of the two most famous is the 3–4–5 right triangle, where 3 2 + 4 2 = 5 2. Special right triangles are right triangles with additional properties that make calculations involving them easier. Right triangles obey the Pythagorean theorem: the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse: a 2 + b 2 = c 2, where a and b are the lengths of the legs and c is the length of the hypotenuse. ![]() The other two sides are called the legs or catheti (singular: cathetus) of the triangle. ![]() The side opposite to the right angle is the hypotenuse, the longest side of the triangle.
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