1. 1. Two points determine a straight line. 2. Between two points, the line segment is the shortest. ? There is one and only one straight line perpendicular to this straight line. 4, the same angle is equal, and the two straight lines are parallel. ? 5. At a point outside the straight line, there is one and only one straight line parallel to this straight line. 6. The corresponding edges and angles of congruent triangles are equal respectively. 7. Edge axiom (SSS): congruence of two triangles with three corresponding equilateral sides. 8. These two straight lines are parallel and the included angle is equal. 9, no * * * line three points to determine a circle.

Second, the right 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, 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 6: In a right triangle, if there is an acute angle equal to 30, then the right-angled side it faces is equal to half of the hypotenuse. In a right triangle, if there is a right-angled side equal to half of the hypotenuse, then the acute angle of this right-angled side is equal to 30. Isosceles triangle:

1. The number of two base angles of an isosceles triangle is equal (abbreviated as "equilateral equilateral angle"). 2. The bisector of the vertex, the midline of the bottom and the high coincidence of the bottom of the isosceles triangle (referred to as "the three-line unity property of the isosceles triangle"). 3. The bisectors of the two bottom angles of the 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 height of one waist 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 an isosceles triangle to two waists is equal to the height of one waist (proved by equal area method). 7. An isosceles triangle is an axisymmetric figure with only one axis of symmetry (when it is not an equilateral triangle), the line where the bisector of the top angle is located is its axis of symmetry, and an equilateral triangle has three axes of symmetry. 8. The square of the waist in an isosceles triangle is equal to the square of the height plus half of the square of the base of an equilateral triangle [1]:

(1) The equilateral triangle is an acute triangle, and the internal angles of the equilateral triangle are all equal, which are all 60.

(2) The midline, height line and angular bisector of each side of an equilateral triangle coincide (the three lines are combined) (3) An equilateral triangle is an axisymmetric figure with three symmetry axes, and the symmetry axis is the straight line where the midline, height line or angular bisector of each side is located. (4) The center of gravity, inner heart, outer heart and vertical center of an equilateral triangle coincide at one point, which is called the center of the equilateral triangle. (Four Centers in One) (5) The sum of the distances from any point to three sides in an equilateral triangle is constant (equal to its height) (6) An equilateral triangle has all the properties of an isosceles triangle. (Because equilateral triangles are special isosceles triangles) There are examples in front of the rest of the books, which are simple and common.