The sum of any two sides of a triangle is greater than the third side, and the difference between any two sides is less than the third side.

It can be expressed by letters as follows: a+b \ u003ec, a+c \ u003eb, b+c \ u003ea; |a-b|\u003cc，|a-c|\u003cb，|b-c|\u003ca .

First, expand the information:

Triangle is a closed figure composed of three line segments on the same plane but not on the same straight line, which has applications in mathematics and architecture.

Ordinary triangles are divided into ordinary triangles by edges. An isosceles triangle with unequal waist bottom and an isosceles triangle with equal waist bottom are equilateral triangles. According to the angle, there are right triangle, acute triangle and obtuse triangle, among which acute triangle and obtuse triangle are collectively called oblique triangle.

Second, the main features

1. The sum of any two sides of the triangle must be greater than the third side, which also proves that the difference between the two sides of the triangle must be less than the third side.

2. The sum of the internal angles of the triangle is equal to 180 degrees.

3. The bisector of the top corner of the isosceles triangle, the middle line of the bottom edge and the heavy eggplant of the bottom edge are combined together, that is, the three lines are one.

4. The square sum of two right angles of a right triangle is equal to the square-pythagorean theorem of the hypotenuse. The center line of the hypotenuse of a right triangle is equal to half of the hypotenuse.

5. The outer angle of a triangle (the angle formed by one side of the inner angle of the triangle and the extension line of the other side) is equal to the sum of two non-adjacent inner angles.

6. The right-angled side corresponding to the 30-degree angle of a triangle is equal to half of the hypotenuse.

The three sides and angles of a triangle have the following relations.

1. Theorem of the sum of triangle internal angles: the sum of triangle internal angles is equal to 180 degrees.

2. Theorem of the sum of external angles: One external angle of a triangle is equal to the sum of its two non-adjacent internal angles.

3. Right triangle theorem: the sum of squares of two right angles of a right triangle is equal to the square of the hypotenuse.

4. Complement theorem: Italian triangle, the square is equal to the sum of squares of the other two sides minus twice the product of these two sides and the cosine of the corresponding angle of these two sides.

5. Sine theorem: In any triangle, any edge is directly proportional to the sine value of its corresponding angle.

6. Cotangent Theorem: In any triangle, any edge is directly proportional to the cotangent value of its corresponding angle. These relations can be used to solve various attributes of triangles, such as angle, side length and area.

7. There are at least two acute angles among the three internal angles of a triangle.