1, the complementary angles of the same angle or equal angle are equal, and the complementary angles of the same angle or equal angle are equal.

2, the vertex angles are equal

3, judge the conditions of two straight lines parallel:

1) At the same angle, two straight lines are parallel. (2) The internal dislocation angles are equal and the two straight lines are parallel. 3) The internal angles on the same side are complementary and the two straight lines are parallel. (4) If two straight lines are parallel to the third straight line, then the two straight lines are also parallel to each other.

4, the characteristics of parallel lines:

(1) At the same angle, two straight lines are parallel. (2) The internal dislocation angles are equal and the two straight lines are parallel. (3) The internal angles on the same side are complementary and the two straight lines are parallel.

5. Proposition:

(1) Concept proposition:

A statement that judges a thing is called a proposition.

(2) the composition of the proposition

Each proposition consists of two parts: the theme and the conclusion. The topic is what is known; The conclusion is derived from what is known. Propositions are often written as "Ru"

Fruit ... then ... "... In this propositional form, the part beginning with" if "is the title, and the part beginning with" then "is the conclusion.

6. Translation

Translation refers to moving a graph along a certain distance on a plane. This graphic movement is called translation, which does not change the shape and size of the object.

(1) Moving the whole graph along a straight line will produce a new graph with the same shape and size as the original graph.

(2) Every point in the new graph is obtained by moving a point in the original graph, and these two points are corresponding points. The line segments connecting each group of corresponding points are parallel and equal.

Chapter VI Plane Cartesian Coordinate System

1, a word containing two numbers indicates a definite position, where the two numbers each indicate a different meaning. We call this number pair composed of two numbers in sequence an ordered number pair, and write it as (a, b).

2. A point on the number axis can be represented by a number, which is called the coordinate of this point.

3. Draw two axes that are perpendicular to each other and have a common origin on the plane. In this way, we say that the plane rectangular coordinate system is established on the plane, which is called rectangular coordinate system for short. The plane rectangular coordinate system has two coordinate axes, in which the horizontal axis is the X axis and the right direction is the positive direction; The vertical axis is the y axis and the direction is the positive direction. The plane where the coordinate system is located is called the coordinate plane, and the common origin of the two coordinate axes is called the origin of the plane rectangular coordinate system. X-axis and Y-axis divide the coordinate plane into four quadrants, the upper right quadrant is called the first quadrant, and the other three parts are called the second quadrant, the third quadrant and the fourth quadrant in turn counterclockwise. Quadrants are bounded by the number axis, and the points and origins on the horizontal and vertical axes do not belong to any quadrant. Generally speaking, the X axis and the Y axis take the same unit length.

3. Coordinate characteristics of special anchor points:

(1). The ordinate of this point on the X axis is zero; The abscissa of a point on the y axis is zero.

(2) The abscissa and ordinate of the points on the bisector of the first and third quadrants are equal; The horizontal and vertical coordinates of the points on the bisector of the second and fourth quadrants are opposite to each other.

(3). If the abscissas of any two points are the same, the connecting line of the two points is parallel to the longitudinal axis; If the vertical coordinates of two points are the same, the straight line connecting the two points is parallel to the horizontal axis.

4. Distance from point to axis and origin

The distance from the point to the X axis is | y | The distance from the point to the Y axis is | x | The distance from the point to the origin is the square of x plus the square of y and then open the root sign;

Characteristics of symmetrical points in plane rectangular coordinate system;

1. The coordinates of points symmetrical about X have the same abscissa and the opposite ordinate.

2. Regarding the coordinates of Y-symmetric points, the ordinate is the same, and the abscissa is the opposite number.

With regard to the coordinates of a point whose origin is central symmetry, the abscissa and abscissa are reciprocal, and the ordinate and ordinate are reciprocal.

The law of points and coordinates on each quadrant and coordinate axis;

The first quadrant: (+,+) The second quadrant: (-,+) The third quadrant: (-,-) The fourth quadrant: (+,-)

X axis positive direction: (+,0)x axis negative direction: (-,0)y axis positive direction: (0, +)y axis negative direction: (0,-)

The ordinate of this point on the X axis is 0, and the abscissa of the Y axis is 0.

Chapter VII Triangle

1, the sum of any two sides of a triangle is greater than the third side, and the difference between any two sides of a shape is less than the third side.

2. The sum of the three internal angles of a triangle is equal to 180 degrees.

3. The two acute angles of a right triangle are complementary.

4. The three bisectors of a triangle intersect at one point, and the three median lines intersect at one point; The straight lines of three heights of a triangle intersect at one point.

5. Conditions for congruence of right triangle:

The hypotenuse and a right-angled side correspond to the congruence of two right-angled triangles, which is called "hypotenuse, right-angled side" or "HL" for short.

As long as any two sides are equal, the two right triangles are congruent.

6. Conditions of triangle congruence:

(1) Three sides correspond to the congruence of two equal triangles, abbreviated as "side" or "SSS".

(2) Two angles and their sides correspond to the congruence of two triangles, which is called "angle" or "ASA" for short.

(3) Two angles and the opposite side of an angle correspond to the congruence of two triangles, which is called "corner edge" or "AAS" for short.

(4) Two triangles with equal angles between two sides are referred to as "corner edge" or "SAS" for short.

27, the characteristics of the isosceles triangle:

(1) A triangle with two equal sides is called an isosceles triangle;

(2) The isosceles triangle is an axisymmetric figure;

(3) The bisector of the top angle, the median line on the bottom and the coincidence on the bottom of the isosceles triangle (also called "three lines in one") are all the symmetry axes of the isosceles triangle.

(4) The two base angles of an isosceles triangle are equal.

(5) The base angle of an isosceles triangle can only be an acute angle.