Triangles. Pythagorean Theorem.

Triangles are geometric figures with three sides and three angles. They are one of the most basic and fundamental shapes in Euclidean geometry. Triangles are classified according to their sides and angles.

In terms of sides, triangles can be equilateral, isosceles or scalene. An equilateral triangle has three equal sides, while an isosceles triangle has two equal sides and one different side. Finally, a scalene triangle has three different sides. As for the angles, triangles can be acute, obtuse or right triangles. An acute triangle has all three acute angles, that is, less than 90 degrees. An obtuse triangle has one obtuse angle, that is, greater than 90 degrees. And a right triangle has a right angle of 90 degrees.

Triangles have unique properties and characteristics. The sum of the internal angles of a triangle is always equal to 180 degrees. Also, any side of a triangle is always less than the sum of the other two sides.

The Pythagorean theorem is an important property of right triangles, which states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Triangles can also be used in practical applications, such as trigonometry. Trigonometric ratios, such as sine, cosine and tangent, are based on the relationships between the sides of a right triangle and its angles.

In addition to their importance in Euclidean geometry, triangles are widely used in a variety of areas, such as architecture, engineering and physics. Their simple and versatile structure makes them key elements in the construction of stable structures and in the description of natural and physical phenomena.