Decision theorem:
1, SSS, which means side by side. A triangle with three equal sides is congruent triangles.
2, SAS, that is, the curve. A triangle with two equal corners is congruent triangles.
3, ASA, that is, corners. Congruence of a triangle with two corners and two sides.
4, AAS, which is the corner. The opposite sides of two angles and one angle correspond to congruences of equal triangles.
5, RHS, that is, right angle, hypotenuse and edge, also known as HL theorem (hypotenuse and right angle edge). In a pair of right-angled triangles, the hypotenuse is equal to the other right-angled side.
The essence of congruent triangles;
The angles corresponding to congruent triangles are equal; The corresponding sides of congruent triangles are equal; The heights of the corresponding sides of congruent triangles are equal; The bisectors of the corresponding angles of congruent triangles are equal; The median lines of the corresponding sides of congruent triangles are equal; The area of congruent triangles is equal; The circumference of congruent triangles is equal; The trigonometric functions of congruent triangles corresponding angles are equal.
Congruent triangles's eight models:
Angular bisector model; Vertical mode; One-line triangular model; Double length midline model; Interception and complementarity; Hand in hand model; Half-angle model; Corner model.
Overview and characteristics of triangles:
Triangle overview:
Triangle is a closed figure composed of three line segments on the same plane but not on the same straight line, which has applications in mathematics and architecture.
Ordinary triangles are divided into ordinary triangles (three sides are unequal) and isosceles triangles (isosceles triangles with unequal waist and bottom and isosceles triangles with equal waist and bottom, that is, equilateral triangles); According to the angle, there are right triangle, acute triangle and obtuse triangle, among which acute triangle and obtuse triangle are collectively called oblique triangle.
Triangular features:
The sum of any two sides of a triangle must be greater than the third side, which also proves that the difference between the two sides of a triangle must be less than the third side. The sum of the internal angles of a triangle is equal to 180 degrees. The bisector of the top angle, the midline of the bottom and the height of the bottom of an isosceles triangle coincide, that is, the three lines are one.
The square sum of two right angles of a right triangle is equal to the square of the hypotenuse-Pythagorean theorem. The center line of the hypotenuse of a right triangle is equal to half of the hypotenuse. The outer angle of a triangle (the angle formed by one side of the inner angle of a triangle and the extension line of the other side) is equal to the sum of two non-adjacent inner angles.