The theoretical basis of algebraic addition and subtraction of 1 is: the rule of removing brackets, the rule of merging similar items, and the multiplication allocation rate.
Rules for removing brackets: If there is a "ten" in front of brackets, remove brackets and the "+"in front of them, and all items in brackets will remain unchanged; If there is a "one" in front of the bracket, remove the bracket and the "one" in front, and change the symbols of everything in the bracket.
2. Similar items: items with the same letters and the same letter index are called similar items.
Merge similar projects:
(1) The concept of merging similar terms: merging similar terms in polynomials into one term is called merging similar terms.
(2) Rules for merging similar items: when the coefficients of similar items are added, the result will be taken as the coefficient, and the index of letters will remain unchanged.
(3) Steps to merge similar projects:
A. find similar projects accurately.
B. Reverse the distribution law, and add the coefficients of similar items together (with brackets) to keep the letters and the indexes of letters unchanged.
C. write the results after the merger.
(4) Note:
A. If the coefficients of two similar items are opposite, the result after merging similar items is 0.
B. Don't leave out items that can't be merged.
C. As long as there are no more similar terms, it is the result (which may be a single term or a polynomial).
Note: The key to merging similar items is to correctly judge similar items.
3, several general steps of algebraic expression addition and subtraction:
(1) List algebraic expressions: enclose each algebraic expression in parentheses and then connect it with a plus sign and a minus sign.
(2) Open brackets according to the rules for opening brackets.
(3) Merge similar items.
4, the general steps of algebraic evaluation:
Algebraic simplification of (1)
(2) Substitution calculation
(3) For some special algebraic expressions, "whole substitution" can be used for calculation.
Intersection line 1, definition: two straight lines intersect, and one of the four angles formed is a right angle, then the two straight lines are perpendicular to each other. One of the straight lines is called the perpendicular of the other straight line, and their intersection point is called the vertical foot.
2. Note:
(1) The vertical line is a straight line.
⑵ The four angles formed by two straight lines with vertical relationship are all 90.
(3) Verticality is a special case of intersection.
(4) Vertical symbols: a⊥b, AB⊥CD.
3. Draw a known straight line with countless vertical lines.
4. There is one and only one straight line perpendicular to the known straight line.
5. Of all the line segments connecting points outside the straight line and points on the straight line, the vertical line segment is the shortest. Simply put: the vertical line is the shortest.
6. The length from a point outside a straight line to the vertical section of the straight line is called the distance from the point to the straight line.
7. One vertex has a common * * *, one side has a common * * *, and the other side is an extension line opposite to each other. Such two angles are called adjacent complementary angles.
There are four pairs of adjacent complementary angles when two straight lines intersect.
8. One vertex has a common * * *, and both sides of the corner are opposite extension lines. These two angles are called antipodal angles. Two straight lines intersect and have two opposite angles. The vertex angles are equal.
Geometry 1, geometry
All kinds of figures abstracted from objects are collectively called geometric figures. Geometric graphics are divided into three-dimensional graphics and plane graphics.
2, three-dimensional graphics
A three-dimensional figure is a geometric figure whose parts are not in the same plane, and it is surrounded by one or more surfaces that can exist in real life. Points become lines, lines become faces, and faces become bodies.
Classification: cylinder, cone, rotating body, sectional body, etc.
3, plane graphics
Plane figure is a kind of geometric figure, which means that all points are on the same plane, such as straight line, triangle and parallelogram. Are basic plane figures.
Classification: circle, polygon, bow, multi-arc.
4. Points, lines, surfaces and bodies
Point: Point is the simplest shape and the most basic component of geometric figure. A point is a figure with only position but no size in space.
Line: A line is a figure composed of countless points.
Face: the trajectory from two points in space to a point with the same distance.
Volume: A polyhedron is a solid surrounded by four or more polygons.
5, straight line, ray, line segment
Straight line: A straight line consists of countless points. There is no end point, extending to both ends indefinitely, and the length cannot be measured. A straight line is an axisymmetric figure.
Ray: refers to a straight line formed by the infinite extension of one end of a line segment. The light has only one endpoint, so the length cannot be measured.
Line segment: refers to the limited part (including two endpoints) between two points on a straight line, which is different from straight lines and rays.
6. Angle: In geometry, an angle is a geometric object composed of two rays with a common endpoint. These two rays are called the edges of an angle, and their common endpoint is called the vertex of the angle.
7. Complementary angle: If the sum of two angles is 90, the two angles are complementary to each other, and the complementary angles of equal angles are equal.
8. Complementary angle: If the sum of the two angles is 180, the two angles are complementary angles, and the complementary angles of equal angles are equal.