Four hearts:
The intersection point of the bisector of the inner angle has the same distance to both sides (the center of the inscribed circle).
The intersection of perpendicular bisector of three sides of an epicentral triangle, and the distance from the triangle to the three vertices is equal (the center of the circumscribed circle).
The intersection of the three center lines of the triangle of gravity, the distance to each vertex is equal to twice the distance to the midpoint of the opposite side.
The intersection of three heights of a vertical triangle.
investigation method
Advantages of a comprehensive survey: high accuracy Disadvantages: Time-consuming and laborious (general survey)
Advantages of sampling survey: low cost and time saving; Disadvantages: the accuracy is affected by the sample.
Concepts of group, individual and sample
Fraction concept
To judge whether a formula is a fraction, the key is to satisfy:
The denominator of 1. fraction must contain letters.
2. The value of denominator cannot be zero. If the denominator is zero, the score is meaningless.
The test method is similar to rational number and irrational number.
mean proportional
If the three quantities A, B and C are connected in proportion, that is, a:b=b:c, then B is called the middle term in the ratio of A and C. ..
B = the square of a*c b = under the plus and minus sign (a * c)
Note that the items in the scale have negative values (line segments and practical problems should be excluded).
Functional concept
Generally speaking, in the process of a change, if there are two variables X and Y, and for each definite value of X, Y has a unique definite value corresponding to it, then Y is said to be a function of X.
Golden section point
Dividing the line segment into two parts satisfies the following requirements:
Short side/long side = long side/full length
Its value is a rational number, expressed as a fraction (√5- 1)/2, which is approximately equal to 0.6 18 (used in practical problems).
Golden Triangle
1. It is an isosceles triangle with two base angles of 72 and a top angle of 36; This triangle is beautiful and standard. The ratio of the base of such a triangle to the length of a waist is the golden ratio: (√5- 1)/2.
2. It is two isosceles triangles with a base angle of 36 and a vertex angle of 108; The ratio of the length of one waist to the bottom of this triangle is the golden ratio: (√5- 1)/2.
Standard deviation
The standard deviation is the arithmetic square root of variance.
similar
Potential mapping:
1. Pay attention to two situations: similarity in the same direction and similarity in the opposite direction.
2. In the plane rectangular coordinate system, if the similarity transformation takes the origin as the similarity center and the similarity ratio is K, then the ratio of the coordinates of the corresponding points of the similar graph is equal to K or-K..
polygon
Internal angle sum (n-2) 180
External angle and 360
See the textbook for the derivation of diagonal n(n-3)/2.