I. Knowledge structure diagram
intersection line
Vertical line of intersection line
Isomorphic angle, internal dislocation angle, ipsilateral internal angle
Parallel lines
Parallel lines and their determination
Determination of parallel lines
Properties of parallel lines
Properties of parallel lines
Propositions and theorems
translate
Two. Definition of knowledge
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:
Isomorphism angle: ∠10 and ∠ 5. Diagonal lines with the same positional relationship like this are called isomorphism 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.
Translation: A figure moves a certain distance in a certain direction in a plane. 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.
Three. Theorems and properties
The nature of antipodal angle: antipodal angle is equal.
Nature of vertical line:
Property 1: There is one and only one straight line perpendicular to the known straight line.
Property 2: Of all the line segments connecting a point outside the straight line and a point on the straight line, the vertical line segment is the shortest.
Parallelism axiom: One and only one straight line is parallel to the known straight line through a point outside the straight line.
Inference of the axiom of parallelism: If two straight lines are parallel to the third straight line, then the two straight lines are also parallel to each other.
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:
Judgment 1: congruent angles are 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.
Chapter VI Plane Cartesian Coordinate System
I. Knowledge structure diagram
Ordered couple
Cartesian coordinates/Cartesian coordinates
Cartesian coordinates/Cartesian coordinates
Coordinate geographical location.
Simple application of coordinate method
Coordinate translation
Two. Definition of knowledge
Ordered number pair: A number pair consisting of two numbers A and B in sequence is called an ordered number pair, and it is recorded as (a, b).
Plane rectangular coordinate system: On a plane, two mutually perpendicular axes with a common origin form a plane rectangular coordinate system.
Horizontal axis, vertical axis and origin: the horizontal axis is called X axis or horizontal axis; The vertical axis is called Y axis or vertical axis; The intersection of the two coordinate axes is the origin of the plane rectangular coordinate system.
Coordinates: For any point P on the plane, the passing P is perpendicular to the X axis and Y axis respectively, and the vertical foot is on the X axis and Y axis respectively. The corresponding numbers a and b are called the abscissa and ordinate of the point p, respectively.
Quadrant: two coordinate axes divide the plane into four parts, the upper right part is called the first quadrant, and the counterclockwise part is called the second quadrant, the third quadrant and the fourth quadrant. The point on the coordinate axis is not in any quadrant.
Chapter VII Triangle
I. Knowledge structure diagram
edge
The height of the line segment associated with the triangle.
median
internal bisector
The sum of internal angles of triangles and polygons.
The sum of the external angles of triangles and polygons.
Two. Definition of knowledge
Triangle: A figure composed of three line segments that are not on the same line and are connected end to end is called a triangle.
Trilateral relationship: the sum of any two sides of a triangle is greater than the third side, and the difference between any two sides is less than the third side.
Height: Draw a vertical line from the vertex of the triangle to the line where the opposite side is located. The line segment between the vertex and the vertical foot is called the height of the triangle.
Midline: In a triangle, the line segment connecting the vertex and the midpoint of its opposite side is called the midline of the triangle.
Angle bisector: the bisector of the inner angle of a triangle intersects the opposite side of the angle, and the line segment between the intersection of the vertex and the angle is called the angle bisector of the triangle.
Stability of triangle: the shape of triangle is fixed, and this property of triangle is called stability of triangle.
Polygon: On the plane, a figure composed of some line segments connected end to end is called polygon.
Interior Angle of Polygon: The angle formed by two adjacent sides of a polygon is called its interior angle.
Exterior angle of polygon: the angle formed by the extension line of one side of polygon and its adjacent side is called the exterior angle of polygon.
Diagonal polygon: The line segment connecting two nonadjacent vertices of a polygon is called diagonal polygon.
Regular polygon: A polygon with equal angles and sides in a plane is called a regular polygon.
Plane mosaic: covering a part of a plane with some non-overlapping polygons is called covering the plane with polygons.
Three. Formulas and attributes
Sum of triangle internal angles: The sum of triangle internal angles is 180.
Properties of the external angle of a triangle:
Property 1: One outer angle of a triangle is equal to the sum of two inner angles that are not adjacent to it.
Property 2: The outer angle of a triangle is larger than any inner angle that is not adjacent to it.
Formula for the sum of polygon internal angles: Is the sum of n polygon internal angles equal to (n-2)? 180
Sum of polygon outer angles: the sum of polygon inner angles is 360.
The number of diagonals of a polygon: (1) Starting from a vertex of an n polygon, (n-3) diagonals can be drawn, and the polygon can be divided into (n-2) triangles.
(2)n sides * * * have diagonal lines. Respondent: 2283759 | Level 2 | 201-4-2117: 56.
1. Understanding of Plane Graphics:
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:
Isomorphism angle: ∠10 and ∠ 5. Diagonal lines with the same positional relationship like this are called isomorphism 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.
Translation: A figure moves a certain distance in a certain direction in a plane. 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.
The nature of antipodal angle: antipodal angle is equal.
Nature of vertical line:
Property 1: There is one and only one straight line perpendicular to the known straight line.
Property 2: Of all the line segments connecting a point outside the straight line and a point on the straight line, the vertical line segment is the shortest.
Parallelism axiom: One and only one straight line is parallel to the known straight line through a point outside the straight line.
Inference of the axiom of parallelism: If two straight lines are parallel to the third straight line, then the two straight lines are also parallel to each other.
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:
Judgment 1: congruent angles are 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.
Triangle: A figure composed of three line segments that are not on the same line and are connected end to end is called a triangle.
Trilateral relationship: the sum of any two sides of a triangle is greater than the third side, and the difference between any two sides is less than the third side.
Height: Draw a vertical line from the vertex of the triangle to the line where the opposite side is located. The line segment between the vertex and the vertical foot is called the height of the triangle.
Midline: In a triangle, the line segment connecting the vertex and the midpoint of its opposite side is called the midline of the triangle.
Angle bisector: the bisector of the inner angle of a triangle intersects the opposite side of the angle, and the line segment between the intersection of the vertex and the angle is called the angle bisector of the triangle.
Stability of triangle: the shape of triangle is fixed, and this property of triangle is called stability of triangle.
Polygon: On the plane, a figure composed of some line segments connected end to end is called polygon.
Interior Angle of Polygon: The angle formed by two adjacent sides of a polygon is called its interior angle.
Exterior angle of polygon: the angle formed by the extension line of one side of polygon and its adjacent side is called the exterior angle of polygon.
Diagonal polygon: The line segment connecting two nonadjacent vertices of a polygon is called diagonal polygon.
Regular polygon: A polygon with equal angles and sides in a plane is called a regular polygon.
Plane mosaic: covering a part of a plane with some non-overlapping polygons is called covering the plane with polygons.
2. Power operation
3. Multiplication of algebraic expressions
4. Multiplication formula
5. Factorization
6. Binary linear equation