Quadrilateral 1. Definition of parallelogram: A quadrilateral with two groups of opposite sides parallel to each other is called a parallelogram.
2. The nature of parallelogram: the opposite sides of parallelogram are equal; The diagonals of parallelogram are equal; Diagonal bisection of parallelogram.
3. Determination of parallelogram: two groups of quadrangles with equal opposite sides are parallelograms; Quadrilaterals whose diagonals bisect each other are parallelograms; Two groups of quadrangles with equal diagonal are parallelograms; A set of quadrilaterals with parallel and equal opposite sides is a parallelogram.
4. The midline of the triangle is parallel to the third side of the triangle, which is equal to half of the third side.
5. The midline of the hypotenuse of a right triangle is equal to half of the hypotenuse.
6. Definition of rectangle: a parallelogram with a right angle.
7. The nature of the rectangle: all four corners of the rectangle are right angles; The diagonals of a rectangle are equally divided. AC=BD
8. Rectangular judgment theorem: a parallelogram with a right angle is called a rectangle; Parallelograms with equal diagonals are rectangles; A quadrilateral with three angles at right angles is a rectangle.
9. Definition of diamond: parallelogram with equal adjacent sides.
10. The nature of the diamond: all four sides of the diamond are equal; The two diagonals of the diamond are perpendicular to each other, and each diagonal bisects a set of diagonals.
The judgement theorem of 1 1. rhombus: A set of parallelograms with equal adjacent sides is a rhombus; Parallelograms with diagonal lines perpendicular to each other are rhombic; A quadrilateral with four equilateral sides is a diamond.
S diamond = 1/2×ab(a and B are two diagonal lines).
12. Definition of a square: a rhombus with right angles or a rectangle with equal adjacent sides.
13. The essence of a square: all four sides are equal and all four corners are right angles. A square is both a rectangle and a diamond.
14. Square judgement theorem: 1. A rectangle with equal adjacent sides is a square. Diamonds with right angles are squares.
15. Definition of trapezoid: A set of quadrangles with parallel opposite sides and another set of non-parallel opposite sides is called trapezoid.
16. Definition of right-angled trapezoid: a trapezoid with a right angle.
17. Definition of isosceles trapezoid: isosceles trapezoid.
18. Properties of isosceles trapezoid: two angles on the same base of isosceles trapezoid are equal; The two diagonals of an isosceles trapezoid are equal.
19. Judgment theorem of isosceles trapezoid: A trapezoid with two equal angles on the same base is an isosceles trapezoid.
Operational multiplication of fractions: take the product of molecular multiplication as the numerator of the product and the product of denominator multiplication as the denominator of the product.
Division: dividing by a fraction is equal to multiplying the reciprocal of this fraction.
Addition and subtraction: ① Addition and subtraction with denominator fraction, denominator unchanged, numerator addition and subtraction. ② Fractions with different denominators shall be divided into fractions with the same denominator first, and then added and subtracted.
Fractional equation: ① The equation with unknown number in denominator is called fractional equation. ② The solution whose denominator is 0 is called the root increase of the original equation.
The case of the root of a linear equation with one variable
Using the discriminant of roots to understand, the discriminant of roots can be written as "△".
One-dimensional linear equation 1 There is only one unknown in an equation, and the exponent of the unknown is 1. Such an equation is called a one-dimensional linear equation.
2. Add or subtract or multiply or divide (non-0) an algebraic expression on both sides of the equation at the same time, and the result is still an equation.
Steps to solve a linear equation with one variable: remove the denominator, shift the term, merge the similar terms, and change the unknown coefficient into 1.
A binary linear equation contains two unknowns, and the degree of the unknowns is 1, which is called a binary linear equation.
Binary linear equations: The equations composed of two binary linear equations are called binary linear equations.
A set of unknown values suitable for binary linear equation is called the solution of this binary linear equation.
The common * * * solution of each equation in a binary linear system of equations is called the solution of this binary linear system of equations.
Methods of solving binary linear equations: substitution elimination method/addition and subtraction elimination method.