1, sine theorem: a/sinA=b/sinB=c/sinC=2R.

2. Cosine theorem: cos A=(b? +c？ -a？ )/2 BC.

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Eight theorems about triangles are as follows:

1. The sum of any two sides of the triangle must be greater than the third side, which also proves that the difference between any 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 vertex, the midline of the bottom and the height of the bottom of the isosceles triangle coincide, 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. A triangle has at least two acute angles.

7. Angle bisector of triangle: the bisector of an angle of triangle intersects with the opposite side of this angle, and the line segment between the vertex and the intersection of this angle.

8. In an isosceles triangle, the bisector of the vertex of the isosceles triangle bisects the base and is perpendicular to the base.

9. Pythagorean inverse theorem: If the three sides of a triangle have the following relationship, then A 2+B 2 = C 2. Then this triangle must be a right triangle. 10. The sum of the outer angles of a triangle is 360 degrees.

1 1. The base and the triangle with the same height have the same area.

12. The area ratio of equilateral triangles is equal to their height ratio, and the area ratio of equilateral triangles is equal to their base ratio.

13. The sum of squares of the lengths of the three center lines of a triangle is equal to 3/4 of the sum of squares of the lengths of its three sides.

14. tanatantbank = tana+tanb+tanc is always satisfied in △ABC.

15. The outer angle of a triangle is larger than any inner angle that is not adjacent to it.

16. The corresponding edges of congruent triangles are equal, and the corresponding angles are equal.

The formula of triangle is:

1, triangle height = area x2+ base.

2. Triangle base = area x2+ height.

3. Calculation formula of triangle area: area = bottom x height +2(s=ah+2).

4. The circumference of an irregular triangle: C=a+b+c(a, B and C are three sides respectively).

5. The circumference of an isosceles triangle: C=2a+b(a is the two sides of the isosceles).

6. The circumference of an equilateral triangle: C=3a(a is three equilateral sides).