First grade mathematics concepts
Real numbers:
—Rational numbers and irrational numbers are collectively called real numbers.
Rational numbers:
Integers and fractions are collectively called rational numbers.
Irrational numbers:
Irrational numbers refer to infinite non-repeating decimals.
Natural numbers:
The numbers 0, 1, 2, 3, 4~ (0 inclusive) representing the number of objects are all called natural numbers.
Number axis:
The straight line that specifies the circular point, positive direction and unit length is called the number axis.
Opposite numbers:
Two numbers with different signs are opposites of each other.
Reciprocals:
Two numbers whose product is 1 are reciprocals of each other.
Absolute value:
The distance between the point representing the number a and the circle point on the number axis is called the absolute value of a. The absolute value of a positive number is itself, the absolute value of a negative number is its opposite, and the absolute value of 0 is 0.
Mathematical theorem formulas
Operation rules of rational numbers
⑴ Addition rule: Add two numbers with the same sign, take the same sign, and add the absolute values ;To add two numbers with different signs, take the sign of the addend with the larger absolute value, and subtract the smaller absolute value from the larger absolute value. The sum of two numbers with opposite signs is 0.
⑵ Subtraction rule: Subtracting a number is equal to adding the opposite of the number.
⑶ Multiplication rule: When two numbers are multiplied together, the numbers with the same sign will be positive, and the numbers with different signs will be negative, and the absolute values ??will be multiplied together; any number multiplied by 0 will get 0.
⑷ Rule of division: dividing by a number is equal to multiplying the reciprocal of the number; when dividing two numbers, the same sign will be positive, and the different signs will be negative, and the absolute value will be divided; 0 is divided by any Any number that is not equal to 0 must be 0.
Angle bisector: A ray drawn from a vertex of an angle can divide the angle into two equal parts. This ray is called the angle bisector of the angle.
Mathematics Chapter 1 Intersecting Lines
1. Adjacent supplementary angles: Among the four angles formed by the intersection of two straight lines, there is a common *** vertex, and there is a common * ** side, such angles are called supplementary angles. Adjacent supplementary angles are angles with special positional and quantitative relationships, that is, adjacent supplementary angles must be supplementary angles, but supplementary angles are not necessarily adjacent supplementary angles.
2. Vertex angle: It is formed by the intersection of two straight lines. The two sides of two angles are opposite extensions of each other, so the opposite angle can also be said to be "the two angles formed by extending the two sides of an angle in opposite directions are called opposite angles".
Properties of opposite vertex angles: opposite vertex angles are equal.
3. Verticality
1. Verticality: When one of the four angles formed by two straight lines is a right angle, the two straight lines are said to be perpendicular to each other. One of them is called the perpendicular line of the other, and their intersection is called the perpendicular foot. Marked as a⊥b
Perpendicularity is a special case of intersection.
2. Properties of perpendicular lines:
①There is and is only one straight line perpendicular to the known straight line through a point;
②Connecting a point outside the straight line and the straight line Among all the line segments at each point, the perpendicular segment is the shortest.
The length of the perpendicular segment from a point outside the straight line to the straight line is called the distance from the point to the straight line.
3. Drawing method: ① One leaning (known straight line) ② Second crossing (fixed point) ③ Three drawing (vertical line)
4. Vertical relationship of space
4. Parallel lines
1. Parallel lines: Two straight lines that do not intersect in the same plane are called parallel lines. Marked as a‖b
2. "Three lines and eight angles": Two straight lines are intercepted by a third straight line
① Isotopic angles: "Same direction and same position" means that two straight lines are in the same direction. Above or below a straight line, on the same side of a third straight line.
② Internal angle: "between both sides" means between two straight lines and on both sides of the third straight line.
③ The internal angles on the same side are "between the same side" that is, between two straight lines and on the same side of the third straight line.
3. Parallel axiom: passing through a point outside a straight line, there is and is only one straight line parallel to this straight line
Corollary of the parallel axiom: if two straight lines are parallel to a third straight line , then these two straight lines are also parallel to each other.
4. How to determine parallel lines
① Two straight lines are intercepted by a third straight line. If the angles are equal, then the two straight lines are parallel;
< p>② If two straight lines are intercepted by a third straight line, if the interior angles are equal, then the two straight lines are parallel;③ If two straight lines are intercepted by a third straight line, if the interior angles are equal complementary, then the two straight lines are parallel;
④ Two straight lines parallel to the same straight line are parallel;
⑤ Two straight lines perpendicular to the same straight line are parallel.
5. Properties of parallel lines:
① Two parallel lines are intercepted by a third straight line, and the angles are equal;
② Two parallel lines If intercepted by a third straight line, the interior angles on the same side are equal;
③ Two parallel lines are intercepted by a third straight line, and the interior angles on the same side are complementary.
6. The distance between two parallel lines: The length of a line segment that is perpendicular to two parallel lines at the same time and sandwiched between the two parallel lines is called the distance between the two parallel lines.
7. Proposition: A statement that judges a thing is called a proposition, which consists of two parts: the proposition and the conclusion.
Five translations
1. Translation: moving a figure a certain distance in a certain direction in a plane. Such graphic movement is called translation.
Explanation: ①. Translation does not change the shape and size of the graphic, but changes the position of the graphic; ② "Moving a graphic a certain distance in a certain direction" means "every point on the graphic moves along the Moved the same distance in the same direction" This is also the key to judging whether a movement is translation. ③The direction of graphic translation is not necessarily horizontal
2. The nature of translation: after translation, the corresponding line segments and corresponding angles are equal respectively, and the line segments connected to the corresponding points are parallel and equal.