The side length formula of isosceles triangle: in △ABC, a? =b？ +c？ The theorem of -2bc×cosA can be transformed into cosA=(b? +c？ -a？ ) 2 years BC.

In an isosceles triangle, two equal sides are called the waist of the triangle and the other side is called the base. The angle between the two waists is called the top angle, and the angle between the waist and the bottom edge is called the bottom angle. The two base angles of an isosceles triangle are equal (abbreviated as "equilateral angles").

The nature of isosceles triangle;

1. The bisector of the top angle, the median line on the bottom edge and the height on the bottom edge of an isosceles triangle coincide (hereinafter referred to as "isosceles triangle with three lines in one").

2. The sum of the distances from any point on the bottom of the isosceles triangle to the two waists is equal to the height of one waist (proved by equal area method).

3. The general isosceles triangle is an axisymmetric figure with only one axis of symmetry, and the line where the bisector of the top angle is located is its axis of symmetry. But an equilateral triangle (a special isosceles triangle) has three axes of symmetry. The straight line where the bisector of each angle is located, the straight line where the three median lines are located, and the straight line where the height is located are the symmetry axes of equilateral triangles.