Intersecting and parallel lines 1. intersection line
In the same plane, there are two positional relationships between two straight lines: intersecting and parallel. If two straight lines have only one common point, they are said to intersect.
2. Vertical line
One of the four angles formed by the intersection of two straight lines is a right angle, that is, the two straight lines are perpendicular to each other, one of which is called the perpendicular of the other straight line, and the intersection point is called the vertical foot.
3. Equidistant angle
Two straight lines A and B are cut by a third straight line C (or the intersection of C of A and B). On the same side of the cutting line C, cut the corners on the same side of the two straight lines A and B.. We call these two angles congruent angles.
4. Inner corner
Two straight lines are cut by a third straight line, and the two corners are on both sides of the cutting line and sandwiched between the two cut straight lines. Diagonal lines with this positional relationship are called inscribed angles.
5. ipsilateral internal angle
The two angles at which two straight lines intersect with the third line are called inner angles on the same side, which are located on the same side of the cutting line and within the cutting line.
6. Parallel lines
In geometry, two straight lines that never intersect (and never coincide) on the same plane are called parallel lines.
The nature of parallel lines: ① Two lines are parallel, and the included angle is equal; ② Two straight lines are parallel and the internal dislocation angles are equal; ③ The two straight lines are parallel and complementary.
7. Translation
Translation means that all points on the map move equidistantly along a straight line in the same plane. This kind of graphic movement is called graphic translation movement, which is called translation for short.
Definition of Binary Linear Equations (1)
Binary linear equation refers to an equation with two unknowns (such as X and Y), and the degree of the unknowns is 1. Two combined linear equations with two unknowns are called binary linear equations.
(2) The solution method of binary linear equation
① Substitution elimination method
② Method of addition, subtraction and elimination
Inequality and inequality group (1) inequality
Using inequality symbols (
(2) the essence of inequality
① symmetry;
② Transitivity;
③ monotonicity of addition, that is, additivity of inequality in the same direction;
④ Monotonicity of multiplication;
⑤ Multiplicity of positive inequality in the same direction;
⑥ Positive inequalities can be multiplied;
⑦ Positive inequalities can be squared;
(3) One-dimensional linear inequality
A formula connected by an inequality symbol contains an unknown number whose degree is 1, whose coefficient is not 0, and whose left and right sides are algebraic expressions is called one-dimensional linear inequality.
(4) One-dimensional linear inequalities
The group of one-dimensional linear inequalities consists of several one-dimensional linear inequalities with the same unknowns.
The division of the same base power is 1. Same base powers's division rule: same base powers divides, the base number remains unchanged, and the exponent is subtracted, that is, (a≠0, m, n is a positive number, m >；; n)。
2. In application, the following points should be noted:
(1) The prerequisite for using the rule is "divisible by same base powers" and 0 is not divisible, so a≠0 is included in the rule.
② Any number that is not equal to 0, whose power of 0 is equal to 1, that is, if (-2.50= 1), then 00 is meaningless.
(3) The power of any number not equal to 0 is -p (p is a positive integer) which is equal to the reciprocal of the power of this number, that is, (a≠0, p is a positive integer), 0- 1, 0-3 is meaningless; When a>0, the value of a-p must be positive; When a<0, the value of a-p can be positive or negative, for example,
④ Pay attention to the operation sequence.
Collection and arrangement of data The step of describing data with histogram (that is, the step of making histogram)
1. Calculate the difference between the maximum and minimum values.
2. Determine the distance and number of groups.
Principle: When the number of data is less than 100, it is divided into 5~ 12 groups according to the number of data.
Group Distance: Divide all data into several groups, and the distance between two endpoints of each group (the range of values of data in the group).
3. Column frequency distribution table
Frequency: The number of data in each group is called frequency.
4. Draw the histogram of frequency distribution.
5. The area of the small rectangle indicates the frequency. The vertical axis is. When grouped at equal intervals, the frequency is usually expressed directly by the height of a small rectangle, that is, the vertical axis is "frequency".
6. Frequency distribution diagram. Draw a frequency distribution line chart according to the frequency distribution chart:
① Take the midpoint of the upper side of each small rectangle and the point on the X axis that is half a group distance from the leftmost and rightmost straight edge. 2 connection.
Point-line-polygon knowledge point 1. Composition of geometric figures
Point: The point where straight lines intersect is the point, which is the most basic figure in geometry.
Line: The intersection line between faces is a line, which can be divided into straight lines and curves.
Face: Surrounding the body is the face, which is divided into plane and curved surface.
Volume: Geometry is also called volume for short.
2. Point to line, line to surface, surface to body.
Representation of points, lines, rays and line segments
In geometry, we often use letters to represent figures.
A dot can be represented by capital letters.
Lowercase letters can represent a straight line.
A ray can be represented by an endpoint and another point on the ray.
The endpoint of a line segment can be represented by two capital letters.
note:
(1) indicates points, lines, rays and line segments, and the points, lines, rays and line segments should be marked before the letters.
(2) Lines and rays have no length, but line segments have length.
(3) A straight line has no endpoint, a ray has one endpoint, and a line segment has two endpoints.
(4) The positional relationship between points and straight lines can be divided into two types:
The point is on a straight line, or a straight line passes through the point.
② The point is outside the straight line, or the straight line does not pass through this point.