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Error-prone knowledge points of mathematics in grade three
Intersecting line and parallel line
1. Properties of parallel lines
Property 1: Two straight lines are parallel and equal to the complementary angle. Property 2: Two straight lines are parallel and the internal dislocation angles are equal. Property 3: Two straight lines are parallel and complementary.
Determination of parallel lines: Determination 1: Same angle is equal and two straight lines are parallel. Decision 2: The internal dislocation angles are equal and the two straight lines are parallel. Judgment 3: The internal angles on the same side are equal and the two straight lines are parallel.
2. Adjacent complementary angles: among the four angles formed by the intersection of two straight lines, two angles with a common vertex and a common edge are adjacent complementary angles.
Diagonal: Two sides of one angle are relative extension lines of another angle, and two angles like this are diagonal to each other.
Perpendicular: When two straight lines intersect at right angles, they are said to be perpendicular to each other, and one of them is said to be perpendicular to the other.
Parallel lines: In the same plane, two disjoint lines are called parallel lines. Conformal angle, internal dislocation angle and ipsilateral internal angle:
3. Isomorphism angles: ∠1and ∠ 5. Diagonal lines with the same positional relationship like this are called isomorphic angles.
Internal angles: ∠2 and ∠6 A pair of angles like this is called an internal angle.
The diagonal lines such as ∠ 2 and ∠ 5 are called ipsilateral internal angles. Proposition: A statement that judges a thing is called a proposition.
4. Translation: In a plane, a figure moves a certain distance in a certain direction. This movement of graphics is called translation transformation, or translation for short.
Corresponding point: every point in the new graphic after translation is obtained by moving a point in the original graphic. Such two points are called corresponding points.
Basic knowledge points of mathematics in grade three
Axisymmetric knowledge point
1. If a graph is folded along a straight line and the parts on both sides of the straight line can overlap each other, then the graph is called an axisymmetric graph;
This straight line is called the axis of symmetry.
2. The symmetry axis of an axisymmetric figure is the perpendicular bisector of a line segment connected by any pair of corresponding points.
3. The distance from the point on the bisector of the angle is equal to both sides of the angle.
4. The distance between any point on the vertical line of the line segment and the two endpoints of the line segment is equal.
5. The point with equal distance from the two endpoints of a line segment is on the middle vertical line of this line segment.
6. The corresponding line segment and the corresponding angle on the axisymmetric figure are equal.
7. Draw an axisymmetric figure about a straight line: find the key points, draw the corresponding points of the key points, and connect the points in the original order.
8. The coordinates of the point (x, y) about the axis symmetry of X are (x, -y).
The coordinates of the point (x, y) that is symmetric about y are (-x, y).
The coordinates of the point (x, y) that is symmetrical about the origin are (-x, -y).
9. The nature of isosceles triangle: the two base angles of isosceles triangle are equal (equilateral and equiangular).
The bisector of the top angle of an isosceles triangle, the height on the bottom edge and the midline on the bottom edge coincide, which is called the integration of the three lines for short.
10. Determination of isosceles triangle: equilateral and equilateral.
1 1. The three internal angles of an equilateral triangle are equal and equal to 60.
12. Determination of equilateral triangle: A triangle with three equal angles is an isosceles triangle.
An isosceles triangle with an angle of 60 is an equilateral triangle.
A triangle with two angles of 60 is an equilateral triangle.
13. In a right triangle, the right angle side of 30 is equal to half of the hypotenuse.
Mathematics knowledge points of grade three
inequality
1. Grasp the basic properties of inequality and use it flexibly;
Add (or subtract) the same algebraic expression on both sides of inequality (1), and the direction of inequality remains the same, that is, if A >；; B, then a+c > b+c，a-c & gt； b-c .
(2) if both sides of the inequality are multiplied by (or divided by) the same positive number, the direction of the inequality remains unchanged, that is, if a >；; B and c>0, then AC & GT200 BC.
(3) If both sides of the inequality are multiplied by (or divided by) the same negative number, the direction of the inequality will change, that is, if a >；; B, and c < 0, ac
2. Comparison size: (A and B represent two real numbers or algebraic expressions respectively)
Generally speaking:
If a>b, then a-b is a positive number; On the other hand, if a-b is positive, then a >；; b；
If a=b, then a-b is equal to 0; On the other hand, if a-b is equal to 0, then a = b；;
If a
Namely: a>b<= = = & gta-b & gt；; 0; a = b & lt= = = & gta-b = 0； aa-b & lt； 0。
3. Solution set of inequality: the value of unknown quantity that can make inequality hold is called the solution of inequality;
All the solutions of an inequality constitute the solution set of this inequality; The process of finding the solution set of inequality is called solving inequality.
4. Representation of the inequality solution set on the number axis: When the inequality solution set is represented by the number axis, the boundary and direction should be determined: ① Boundary: there are solid circles with equal signs and hollow circles without equal signs;
② Direction: large on the right and small on the left.
Solutions of one-dimensional linear equations
1. General method:
Denominator: Denominator refers to the least common multiple of the denominator multiplied by both sides of the equation at the same time.
(2) Remove the brackets: put "+"before the brackets. After removing the brackets and the "+"sign in front of them, the symbols of the items in the original brackets remain unchanged. There is a "-"before the brackets. After removing the brackets and the "-"sign in front of them, the symbols of the original brackets will change. (Replace with the opposite symbol.
③ Shift term: Adding (or subtracting) the same number or the same algebraic expression on both sides of the equation is equivalent to changing the sign of some terms in the equation and moving them from one side of the equation to the other. This deformation is called displacement term.
(4) Merging similar terms: The unary linear equation is formulated into the simplest form by merging similar terms: ax=b(a≠0).
⑤ The coefficient is 1.
2. Mirror image method: the root of the unary linear equation ax+b=0(a≠0) is the value of the independent variable X when its corresponding linear function f(x)=ax+b is 0, that is, the abscissa of the intersection of the linear function mirror image and the X axis.
3. Root formula method: For the unary linear equation ax+b=0(a≠0) about X, the root formula is: X =-B/A.
Integral expression
1. Algebraic formula: Algebraic formula is a general term for monomial and polynomial, and it is a part of rational formula. In rational expressions, there can be five operations, including addition, subtraction, multiplication, division and multiplication, but in algebraic expressions, the divisor cannot contain letters.
multiplication
(1) Power with the same base, with the same base and exponential addition.
(2) the power of the power, the base is unchanged, multiplied by the index.
(3) the product of the power, first multiply each factor in the product, and then multiply the obtained power.
3. Division of algebraic expressions
(1) same base power division, constant base, exponential subtraction.
(2) The zeroth power of any number that is not equal to zero is 1.
Properties of fractions
1. The horizontal line in the middle of the score is called the fractional line, the number above the fractional line is called the numerator, and the number below the fractional line is called the denominator.
Read it as a score.
2. Fractions can be expressed by division formula: for example, half equals 1 divided by 2.
Where 1 numerator is equal to dividend,-fractional line is equal to divisor, denominator of 2 is equal to divisor, and 0.5 fractional value is equal to quotient.
3. Scores can also be expressed as ratios, for example;
Half is equal to 1: 2, where 1 numerator is equal to the previous paragraph,-the fractional line is equal to the comparison number, the denominator of 2 is equal to the latter term, and the value of 0.5 points is equal to the ratio.
4. When the numerator and denominator are multiplied or divided by the same number at the same time (except 0), the fractional value will not change.
Therefore, each score has an infinite number of equal parts. Using this property, we can be on and off.
5. Fractions are either finite decimals or infinite cyclic decimals, and infinite acyclic decimals like π cannot be replaced by fractions.