What are the triangles?

Ivan Orlov
Ivan Orlov
April 15, 2013
What are the triangles?

A triangle (from the point of view of Euclidean space) is such a geometrical figure, which is formed by three segments connecting three points that are not lying on one straight line. The three points that formed the triangle are called its vertices, and the segments connecting the vertices are called the sides of the triangle. What are the triangles?

Equal triangles

There are three signs of equality of triangles. What triangles are called equal? These are those with:

  • the two sides and the angle between these sides are equal;
  • equal to one side and two adjacent angles;
  • all three sides are equal.

Right triangles have the following signs of equality:

  • acute angle and hypotenuse;
  • on the acute angle and the leg;
  • along two legs;
  • on a hypotenuse and a leg.

What are the triangles

By the number of equal sides a triangle can be:

  • Equilateral. This is a triangle with three equal sides. All angles in an equilateral triangle are 60 degrees. In addition, the centers of the circumscribed and inscribed circles coincide.
  • Unequilateral. A triangle with no equal sides.
  • Isosceles. This is a triangle with two equal sides. The two sides are the same side, and the third side is the base. In such a triangle the bisector, the median and the height coincide, if they are lowered to the base.

The magnitude of the angles of a triangle can be:

  1. Obtuse - when one of the corners has a size of more than 90 degrees, that is, when it is blunt.
  2. Acute - if all three angles in the triangle are acute, that is, they have a magnitude less than 90 degrees.
  3. Which triangle is called rectangular? This is one that has one right angle equal to 90 degrees. In it two sides will be called the legs, which form this angle, and the hypotenuse is the side opposite to the right angle.

Basic properties of triangles

  1. Against the smaller side there is always a smaller angle, and a larger angle always lies against the larger side.
  2. Equal angles always lie against equal sides, and different angles always lie against different sides. In particular, in an equilateral triangle all angles have the same value.
  3. In any triangle, the sum of the angles is 180 degrees.
  4. The external angle can be obtained if the triangle to continue one of its sides. The magnitude of the outer angle will be equal to the sum of the inner corners not adjacent to it.
  5. The side of the triangle is greater than the difference of its two other sides, but less than their sum.

In the spatial geometry of Lobachevsky, the sum of the angles of a triangle will always be less than 180 degrees. On the sphere, this value is greater than 180 degrees.