(1) line
straight line
A straight line has no end; Infinitely long; You can draw countless lines after one o'clock, and only one straight line after two o'clock.
ray
Ray has only one endpoint; Infinitely long.
line segment
A line segment has two endpoints, which are part of a straight line; Limited length; In the connection between two points, the segment is the shortest.
Parallel lines
On the same plane, two lines that do not intersect are called parallel lines.
The vertical lines between two parallel lines are equal in length.
vertical line
When two straight lines intersect at right angles, they are said to be perpendicular to each other, one of them is said to be perpendicular to the other, and the intersection point is called vertical foot.
The length of a vertical line drawn from a point outside a straight line is called the distance from that point to the straight line.
(2) Angle
Two rays drawn from a point form a figure called an angle. This point is called the vertex of the angle, and these two rays are called the edges of the angle.
Classification of angles
Acute angle: An angle less than 90 is called acute angle.
Right angle: An angle equal to 90 is called a right angle.
Oblique angle: an angle greater than 90 and less than180 is called obtuse angle.
Flat angle: The two sides of an angle form a straight line, and the angle formed at this time is called a flat angle. Boxer 180.
Fillet: One side of the corner rotates once and coincides with the other side. Fillet 360.
Second, the plane graphics
1. rectangle
(1) function
A quadrilateral with equal opposite sides and four right angles. There are two axes of symmetry.
(2) Calculation formula
c=2(a+b)
s=ab
2. Square
(1) Function:
A quadrilateral with four equal sides and four right angles. There are four axes of symmetry.
(2) Calculation formula
c=4a
s=a2
Step 3: Triangle
(1) function
A figure surrounded by three line segments. The sum of internal angles is 180 degrees. The triangle is very stable. A triangle has three heights.
(2) Calculation formula
s=ah/2
(3) Classification
Divide by angle
Acute triangle: all three angles are acute.
Right triangle: One angle is a right angle. The two acute angles of an isosceles triangle are 45 degrees each, and it has an axis of symmetry.
Obtuse triangle: One angle is obtuse.
Divide by edge
Unequal triangle: The three sides are not equal in length.
Isosceles triangle: two sides are equal in length; The two bottom angles are equal; There is an axis of symmetry.
Equilateral triangle: all three sides are equal in length; All three internal angles are 60 degrees; There are three axes of symmetry.
4. Parallelogram
(1) function
Two sets of quadrilaterals parallel to opposite sides.
The opposite sides are parallel and equal. Diagonal angles are equal, and the sum of degrees of two adjacent angles is 180 degrees. Parallelogram is easy to deform.
(2) Calculation formula
S = ah
5. trapezoidal
(1) function
There is only one set of quadrilaterals with parallel sides.
The center line is equal to half of the sum of the upper and lower bottoms.
An isosceles trapezoid has an axis of symmetry.
(2) Formula
s=(a+b)h/2=mh
6. circle
Understanding of (1) circle
A curved figure on a plane.
The point of the center of the circle is called the center of the circle. Generally represented by the letter o.
Radius: The line segment connecting the center of the circle and any point on the circle is called radius. Generally expressed by R.
In the same circle, there are countless radii, and each radius has the same length.
The line segment passing through the center of the circle with both ends on the circle is called the diameter. Generally represented by D.
The same circle has countless diameters, all of which are equal.
In the same circle, the diameter is equal to the length of two radii, that is, d=2r.
The size of a circle depends on its radius. A circle has countless axes of symmetry.
(2) Drawing a circle
Separate the two feet of the compass and determine the distance (radius) between the two feet;
Fix a foot on a point (that is, the center of the circle) with a needle tip;
Turn one foot with the tip of a pencil once and draw a circle.
(3) the circumference of a circle
The length of the curve forming a circle is called the circumference of the circle.
The ratio of the circumference to the diameter of a circle is called pi. Represented by the letter ∏.
(4) the area of the circle
The size of the plane occupied by a circle is called the area of the circle.
(5) Calculation formula
d=2r
r=d/2
c=∏d
c = 2 r
s=∏r2
7. Fan shape
Understanding of (1) Plate
A figure surrounded by an arc and two radii passing through both ends of the arc is called a fan.
The part between two points AB on the circle is called arc, which is pronounced as "arc AB".
The angle of the vertex at the center of the circle is called the central angle.
In the same circle, the size of the sector is related to the central angle of the sector.
The sector has an axis of symmetry.
(2) Calculation formula
s = n R2/360
8. Ring shape
(1) function
It is formed by subtracting two concentric circles with different radii, and there are countless symmetry axes.
(2) Calculation formula
s = ∏( R2 R2)
9. Axisymmetric graphics
(1) function
If a graph is folded in half along a straight line, the graphs on both sides can completely overlap, and this graph is an axisymmetric graph. The straight line where the crease lies is called the symmetry axis.
A square has four axes of symmetry, and a rectangle has two axes of symmetry.
An isosceles triangle has two axes of symmetry and an equilateral triangle has three axes of symmetry.
An isosceles trapezoid has one axis of symmetry, and a circle has countless axes of symmetry.
The diamond has four axes of symmetry, and the fan has one axis of symmetry.
3D graphics
(1) cuboid
1. feature
All six faces are rectangles (sometimes two opposite faces are squares).
The areas of the opposite sides are equal, and the lengths of the four opposite sides of 12 are equal.
There are eight vertices.
The lengths of three sides intersecting at a vertex are called length, width and height respectively.
An edge where two faces intersect is called an edge.
The point where three sides intersect is called a vertex.
If you put a cuboid on the desktop, you can only see three faces at most.
The total area of six faces of a cuboid or cube is called its surface area.
2. Calculation formula
s=2(ab+ah+bh)
V=sh
V=abh
(2) Cube
1. feature
All six faces are squares.
The areas of the six faces are equal.
12 sides, all equal in length.
There are eight vertices
A cube can be regarded as a special cuboid.
2. Calculation formula
S table =6a2
v=a3
(3) Cylinder
1. Understanding cylinders
The upper and lower surfaces of a cylinder are called the bottom surface.
A cylinder has a surface called a side.
The distance between the two bottom surfaces of a cylinder is called the height.
Step-by-step method: More materials are actually used than the calculated results. Therefore, when you want to keep numbers, the omitted digits are 4 or less, and you must go forward 1. This approximate method is called step-by-step method.
2. Calculation formula
S side =ch
S table =s side +s bottom ×2
v=sh/3
(4) Cone
1. Understanding of Cone
The bottom of the cone is a circle, and the side of the cone is a surface.
The distance from the apex of the cone to the center of the bottom surface is the height of the cone.
Measuring the height of the cone: firstly, lay the bottom of the cone flat, place a flat plate horizontally above the apex of the cone, and measure the distance between the flat plate and the bottom vertically.
Enlarge the side of the cone to get a sector.
2. Calculation formula
v=sh/3
(5) Ball
1. Understanding
The surface of a sphere is a curved surface, called a sphere.
Like a circle, the ball also has a center, which is represented by O.
The line segment from the center of the sphere to any point on the sphere is called the spherical radius, which is denoted by R, and each radius is equal.
The line segment passing through the center of the sphere and having both ends on the sphere is called the diameter of the sphere, which is represented by d, each diameter is equal, and the length of the diameter is equal to twice the radius, that is, d=2r.
2. Calculation formula
d=2r