triangle
a polygon with three sides and three angles
A triangle is a geometric figure that has three sides and three angles. It is one of the simplest and most basic shapes in geometry, and it has many applications in various fields of mathematics, science, and engineering. The study of triangles is an important part of elementary geometry, and it is also an essential topic in higher-level mathematics and physics.
Triangles can be classified according to their sides and angles. Based on their sides, triangles can be categorized as equilateral, isosceles, and scalene. Equilateral triangles have three sides of equal length, while isosceles triangles have two sides of equal length. Scalene triangles have three sides of different lengths. Based on their angles, triangles can be classified as acute, right, and obtuse. An acute triangle has all three angles less than 90 degrees, a right triangle has one angle equal to 90 degrees, and an obtuse triangle has one angle greater than 90 degrees.
The properties of triangles are governed by various geometrical theorems. For instance, the Pythagorean theorem holds that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. The Law of Cosines can be used to calculate the sides and angles of any triangle, while the Law of Sines is used to determine the length of the side opposite a given angle.
In summary, triangles are an important geometric shape with many properties that are studied in geometry and other fields of mathematics.
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