1, theorem of sum of interior angles of triangle: In a triangle, the sum of three interior angles is always equal to 180 degrees. If all three angles are equal, then each angle is 180 degrees divided by 3, which is 60 degrees.

2. equilateral triangle: if all three sides are equal in length, then these three angles must be equal. This is because in an equilateral triangle, the distance from each vertex to the midpoint of the opposite side is equal, so their corresponding angles are also equal.

3. Isosceles triangle: In an isosceles triangle, the two base angles are equal. This is because the center line of the bottom edge divides the top angle into two equal parts, so the two bottom angles are also equal.

4. Use parallel lines: If two parallel lines are cut by a third straight line, they are equal to the complementary angle (or internal dislocation angle). In a quadrilateral, if two opposite sides are parallel, then two opposite corners are equal.

5. Through trigonometric function: In a right triangle, trigonometric function can be used to prove that the angles are equal. For example, sine function sin(A)=sin(B) can be used to prove that two angles A and B are equal.

6. Use a four-point * * * circle: If all four points are on the same circle, then the diagonals are complementary, that is, the diagonal of one angle is equal to the complementary angle of another angle.

Triangle is a kind of geometric figure, which is a closed figure composed of three line segments that are not on the same line. Triangles have important applications in mathematics and physics.

The nature of the triangle includes the following points:

1, and the sum of the internal angles of the triangle is 180 degrees, that is, the sum of the three internal angles is equal to 180 degrees.

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

3. Triangle is stable, that is, its shape and size are not easy to change when it is acted by external force.

4. Triangle can be divided into acute triangle, right triangle and obtuse triangle.

5. There are three high lines, three middle lines, three angular bisectors and three middle vertical lines on the side of a triangle.

6. Triangle has special points such as center of gravity, vertical center, external center, internal center and transverse center.

7. Triangles have similar properties, that is, the ratio of the corresponding sides of two similar triangles is equal, and the corresponding angles are also equal.

8. The triangle is congruent, that is, the two sides corresponding to congruent triangles are equal, and the corresponding angles are equal.