Triangle knowledge concept 1, 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.
2. 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.
3. Height: Draw a vertical line from the vertex of the triangle to the line where the opposite side is located, and the line segment between the vertex and the vertical foot is called the height of the triangle.
4. midline: in a triangle, the line segment connecting a vertex and its relative midpoint is called the midline of the triangle.
5. Angular bisector: The bisector of the inner angle of a triangle intersects the opposite side of this angle, and the line segment between the vertex and the intersection of this angle is called the angular bisector of the triangle.
6. Stability of triangle: The shape of triangle is fixed, and this property of triangle is called stability of triangle.
7. Polygon: On the plane, a figure composed of some line segments connected end to end is called polygon.
8. Interior Angle of Polygon: The angle formed by two adjacent sides of a polygon is called its interior angle.
9. 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.
10, diagonal of polygon: the line segment connecting two non-adjacent vertices of polygon is called diagonal of polygon.
1 1, regular polygon: a polygon with equal angles and sides in a plane is called a regular polygon.
12, plane mosaic: a part of the plane is completely covered by some non-overlapping polygons, which is called covering the plane with polygons.
13, formula and properties:
(1) Sum of internal angles of triangle: The sum of internal angles of triangle is 180.
(2) the nature of the triangle exterior angle:
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.
(3) Formula for the sum of polygon internal angles: the sum of polygon internal angles is equal to 180.
(4) Sum of polygon external angles: the sum of polygon external angles is 360.
(5) Number of diagonal lines of a polygon: ① Starting from a vertex of a polygon, a diagonal line can be drawn to divide the polygon into triangles. ② The polygon * * * has a diagonal line.
Location and coordinates 1, determine the location.
In a plane, two data are usually needed to determine the position of an object.
2. Plane rectangular coordinate system
Meaning: In a plane, two mutually perpendicular axes with a common origin form a plane rectangular coordinate system.
(2) Usually, the two number axes are placed in horizontal and vertical positions respectively, and the right and upward directions are the positive directions of the two number axes respectively. The horizontal axis is called X axis or horizontal axis, and the vertical axis is called Y axis and vertical axis, both of which are collectively called coordinate axes, and their common origin O is called the origin of rectangular coordinate system.
③ Establish a plane rectangular coordinate system, and the points on the plane can be represented by a set of ordered real number pairs.
(4) In the plane rectangular coordinate system, two coordinate axes divide the coordinate plane into four parts, the upper right part is called the first quadrant, and the other three parts are called the second quadrant, the third quadrant and the fourth quadrant counterclockwise, and the points on the coordinate axes are not in any quadrant.
⑤ In the rectangular coordinate system, for any point on the plane, there is a unique ordered real number pair (that is, the coordinates of the point) corresponding to it; Conversely, for any ordered real number pair, there is a unique point on the plane corresponding to it.
3. Axisymmetry and coordinate changes
Regarding the coordinates of two points about the axis symmetry of X, the abscissa is the same, and the ordinate is opposite; With regard to the coordinates of two points symmetrical about the Y axis, the ordinate is the same, and the abscissa is opposite.
Data analysis 1, average
① Generally speaking, for the number n, x 1x2...xn, we call (x 1+x2++xn) the arithmetic average of several n, and the average is abbreviated as.
② In practical problems, the "importance" of each data in a set of data may be different, so when calculating the average of this set of data, each data is often given a weight, which is called weighted average.
2. Median and mode
① Median: generally, n data are arranged in order of size, and the data in the middle position (or the average of the two data in the middle) is called the median of this group of data.
② The data with the highest frequency in a group of data is called the pattern of this group of data.
③ Average, median and mode are all statistics that describe the trend in data set.
(4) When calculating the average, all the data participate in the operation, which can make full use of the information provided by the data, so it is commonly used in real life, but it is easily influenced by extreme values.
⑤ Median has the advantage of simple calculation and little influence by extreme value, but it can't make full use of all data information.
⑥ When the number of repetitions of each data is roughly equal, the pattern often has no special meaning.
3. Analyze the concentration trend of data from the statistical chart.
4. Degree of data dispersion
① In real life, people not only pay attention to the concentration trend of data, but also pay attention to the degree of dispersion of data, that is, the degree of deviation from the concentration trend. The difference between the largest data and the smallest data in a set of data (called range) is a statistic that describes the degree of data dispersion.
② Mathematically, the dispersion degree of data can also be described by variance or standard deviation.
③ Variance is the average of the square of the difference between each data and the average.
(4) where x 1, the mean of x2 ... xn, s2 is the variance, and the standard deviation is the arithmetic square root of variance.
⑤ Generally speaking, the smaller the range, variance or standard deviation of a set of data, the more stable it is.