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A triangle is a basic geometric shape that consists of three sides and three angles. It is a polygon with three vertices and three line segments connecting them. Triangles are one of the fundamental shapes in geometry and have various properties and classifications based on their side lengths and angle measurements.
The sum of the interior angles of a triangle is always 180 degrees. The side opposite to the largest angle is the longest side and is known as the hypotenuse in a right triangle. Triangles can be classified based on their side lengths as equilateral, isosceles, or scalene triangles. An equilateral triangle has three equal sides and three equal angles of 60 degrees each. An isosceles triangle has two equal sides and two equal angles. A scalene triangle has three unequal sides and three unequal angles.
Triangles also have different classifications based on their angles. A right triangle has one angle measuring 90 degrees. An acute triangle has all three angles measuring less than 90 degrees, and an obtuse triangle has one angle measuring greater than 90 degrees.
Triangles have numerous applications in mathematics, physics, engineering, and other fields. They serve as the building blocks for more complex geometric shapes and are extensively studied in trigonometry, which deals with the relationships between angles and side lengths in triangles.