Second, nature.

1. The two base angles of an isosceles triangle are equal. (abbreviated as "equilateral angle") 2. The bisector of the top angle, the median line on the bottom and the height on the bottom of an isosceles triangle coincide (referred to as "three lines in one") 3. The bisectors of the two base angles of an isosceles triangle are equal. (The midline of the two waists is equal, and the height of the two waists is equal. ) 4. The distance from the perpendicular to the bottom of the isosceles triangle to the waist is equal. 5. The included angle between the waist height and the bottom of an isosceles triangle is equal to half of the top angle. 6. 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 (it needs to be proved by the equal area method). 7. An isosceles triangle is an axisymmetric figure with only one axis of symmetry, and the straight line where the bisector of the top angle is located is its axis of symmetry.

2. equilateral triangle: if one of them is satisfied and the other is satisfied, it is a regular triangle (also called equilateral triangle): 1. These three sides are equal in length. The degree of triangle is 60 degrees.

Properties of equilateral triangle

1) The internal angles of the triangle are all equal, which are all 60 degrees.

2) The midline, height line and bisector of each side of an equilateral triangle coincide (three lines are one).

3) An equilateral triangle is an axisymmetric figure with three axes of symmetry, and the axis of symmetry is the straight line where the median line, height line or diagonal bisector of each side is located.

Right triangle: A triangle with an angle of 90 is called a right triangle.

A right triangle is a special triangle, which has some special properties besides those of a general triangle: property 1: The sum of squares of two right angles of a right triangle is equal to the square of the hypotenuse. (Pythagorean Theorem Property 2: In a right triangle, the two acute angles are complementary. Property 3: In a right triangle, the median line on the hypotenuse is equal to half of the hypotenuse (that is, the outer center of the right triangle is located at the midpoint of the hypotenuse, and the radius of the circumscribed circle r = c/2). Property 4: The product of two right angles of a right triangle is equal to the product of the hypotenuse and the height of the hypotenuse. Property 5: In a right triangle, the right angle side of 30 is equal to half of the hypotenuse.

Triangle: A closed figure consisting of three line segments that are not on the same line and are connected end to end is called a triangle. A figure enclosed by three straight lines on a plane or three arcs on a sphere. The figure surrounded by three straight lines is called a plane triangle; A figure surrounded by three arcs is called a spherical triangle, also known as a triangle.

Property: the sum of the angles in the triangle is 180 degrees;

One outer angle of a triangle is equal to the sum of the other two inner angles;

One outer angle of a triangle is larger than the other two inner angles.