The second grade math mind map Chapter 1 The second grade math knowledge points 1. consistent
1. Definition: Two graphs that can completely overlap are called congruent graphs, or congruent graphs for short.
2. The graphics obtained after graphic transformation such as folding, translation and rotation must be the same as the original graphics. On the contrary, after the above transformation, two congruent figures will be able to overlap each other.
Second, congruent polygons
1. Definition: Polygons that can completely overlap are called congruent polygons. Overlapping points are called corresponding vertices, overlapping edges are called corresponding edges, and overlapping angles are called corresponding angles.
2. Nature:
(1) congruent polygons have equal sides and angles.
(2) The areas of congruent polygons are equal.
Third, congruent triangles.
1, congruence symbol:. As shown in the figure, it is not: △ ABC △ ABC. Reading: All triangles ABC are equal to triangle ABC.
2, congruent triangles's judgment theorem:
(1) Two triangles with two sides corresponding to their included angles are congruent. (i.e. SAS, corner edge)
(2) Two triangles with two corners, with equal sides. (ASA, corner corner)
(3) Two triangles with two angles and opposite sides of one angle are congruent. (that is, AAS, corner edge)
(4) Two triangles corresponding to three equilateral sides are congruent. (SSS, side by side)
(5) Two right-angled triangles with a hypotenuse and a right-angled side are congruent. (i.e. HL, hypotenuse and right angle)
3, the nature of congruent triangles:
(1) congruent triangles has equal sides and angles.
(2) The circumference and area of congruent triangles are equal.
(3) The median line, height and bisector of the corresponding angle of congruent triangles are all equal.
4. The role of congruent triangles:
(1) is used to directly prove that the line segments are equal and the angles are equal.
(2) It is used to prove the parallel relationship and vertical relationship of straight lines.
(3) It is used to measure the distance that people can't reach.
(4) Used to indirectly prove special graphics. (such as proving isosceles triangle, equilateral triangle, parallelogram, rectangle, diamond, square, trapezoid, etc.). ).
(5) Used to solve the problem about equal product.
The main feature of a triangle is 1. 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.
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. The right-angled side corresponding to the 30-degree angle of a triangle is equal to half of the hypotenuse.
7. There are at least two acute angles among the three internal angles of a triangle.
8. The three bisectors of a triangle intersect at one point, the straight lines of three high lines intersect at one point, and the three middle lines intersect at one point.
9. Pythagorean inverse theorem: If three sides of a triangle have the following relationship: A 2+B 2 = C 2. Then this triangle must be a right triangle.
10. Is the sum of the outer angles of the triangle 360? .
1 1. The areas of triangles with equal base and height are equal.
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.
17. At least one angle in the triangle is greater than or equal to 60 degrees, and at least one angle is less than or equal to 60 degrees. (including equilateral triangle)
18.△ABC, there is always tan (a/2)+tan (b/2) tan (a/2)+tan (c/2) = sec (a/2) 2.
19. The center of gravity of a triangle is the intersection of the three midlines of the triangle.
20. The heart of a triangle is the intersection of the bisectors of the three internal angles of the triangle.
2 1. The outer center of a triangle refers to the intersection of the vertical lines of three sides of the triangle.
22. The intersection of straight lines with three heights of a triangle is called the vertical center of the triangle.
23. The intersection of two bisectors of the outer angle and another bisector of the inner angle of a triangle is called the edge center of the triangle.
24. Any midline of a triangle divides the triangle into two triangles with equal areas.
25. Triangles are relatively stable and not easily deformed.