1, frequency and frequency: frequency =, the sum of each group of frequencies is equal to the total, and the sum of each group of frequencies is equal to 1.
2. Histogram of frequency distribution: You can read charts, calculate and complete histograms.
Auxiliary line method
People say that geometry is difficult, and it is difficult in auxiliary lines. The auxiliary line is a dotted line, so be careful not to change it when drawing.
How to add auxiliary lines? Master theorems and concepts. We must study hard and find out the rules by experience.
There is an angular bisector in the picture, which can be perpendicular to both sides. Perpendicular bisector is a line segment that usually connects the two ends of a straight line.
Angle bisector parallel lines, isosceles triangles add up. Angle bisector plus vertical line, try three lines.
The two midpoints of a triangle are connected to form a midline. A triangle has a midline and the midline extends.
A parallelogram appears and the center of symmetry bisects the point. It needs to be proved that the line segment is double-half, and extension and shortening can be tested.
Hunan Education Press Grade 8 Mathematics Volume II (II)
Graphics and coordinates
1, symmetry of point:
Regarding the axis symmetry point of X, the abscissa is opposite and the ordinate is equal;
Regarding the point of Y axis symmetry, the abscissa is equal and the ordinate is opposite;
For a point with symmetrical origin, the abscissa and ordinate are opposite.
For example, there is a point P(a, b) in the rectangular coordinate system, and the point P is symmetric about X as P 1(a, -b), the point P is symmetric about Y as P2(-a, b), and the point P is symmetric about the origin as P3(-a, -b).
Solution: when equal? =? Link, on the contrary, the sum of the two expressions =0.
2. Coordinate translation: left and right translation: abscissa right plus left minus, ordinate unchanged;
Up and down translation: the abscissa is unchanged, and the ordinate is increased or decreased.
For example, a point P(a, b) in a rectangular coordinate system is translated by H units to the left, and the coordinate becomes P(a-h, b), and translated by H units to the right, and the coordinate becomes P(a+h, b); If you translate H units up, the coordinates will become P(a, b+h), and if you translate H units down, the coordinates will become P(a, b-h). For example, if the point A(2,-1) is shifted up by 2 units and then shifted to the right by 5 units, the coordinate becomes A (7, 1).
3. In the plane rectangular coordinate system, the axisymmetric and translational figures will be drawn, and the coordinates of the vertices of the figures will be written.
4. A plane rectangular coordinate system will be established, and the relevant positions will be represented by coordinates.
5. There is a one-to-one correspondence between points on the plane and ordered real number pairs.
Hunan Education Press Eighth Grade Mathematics Volume II Content (3)
Determination of Special Quadrilateral
(1) parallelogram:
Methods 1 Two groups of parallelograms with parallel opposite sides are parallelograms.
As shown in the figure, ∫AB‖CD, AD‖BC,? The quadrilateral ABCD is a parallelogram.
Method 2 Two groups of quadrangles with equal opposite sides are parallelograms.
As shown in the figure, AB = CD, AD=BC,? The quadrilateral ABCD is a parallelogram.
Methods Two groups of quadrangles with equal three diagonals are parallelograms.
As shown, ∵? A=？ c，？ B=？ d，？ The quadrilateral ABCD is a parallelogram.
Method 4 A set of parallelograms with equal opposite sides is a parallelogram.
As shown in the figure, ∫AB‖CD, AB=CD,? The quadrilateral ABCD is a parallelogram.
Or ∵AD‖BC, AD=BC,? The quadrilateral ABCD is a parallelogram.
Method 5 The quadrangles whose diagonals bisect each other are parallelograms.
As shown in the figure, OA = OC, OB=OD,? The quadrilateral ABCD is a parallelogram.
② Rectangular:
Method 1 A quadrilateral with three right angles is a rectangle.
Method 2 Parallelograms with equal diagonals are rectangles.
③ diamonds:
Method 1 A quadrilateral with four equilateral sides is a diamond.
Methods The parallelogram with two diagonal lines perpendicular to each other is a diamond.
④ Square
Method 1 A diamond with a right angle is a square.