Knowledge points in the first volume of junior high school mathematics
A preliminary understanding of graphics
A, three-dimensional graphics and plane graphics
1, cuboids, cubes, spheres, cylinders and cones are all three-dimensional figures. In addition, prisms and pyramids are also common three-dimensional figures.
2. Rectangular, square, triangle and circle are all plane figures.
3. Many three-dimensional graphics are surrounded by some plane graphics, which can be expanded into plane graphics by proper cutting.
Second, points and lines
1, there is a straight line after two, and there is only one straight line.
2. The line segment between two points is the shortest.
3. The line segment AB at point C is divided into two equal line segments AM and MB, and point M is called the midpoint of line segment AB. Similarly, line segments also have bisectors and quartiles.
4. The figure formed by the infinite extension of line segments in one direction is called ray.
Third, the angle
The 1. angle is a graph composed of two rays with a common endpoint.
2. Rotate around the endpoint until the end edge and the start edge of the angle form a straight line, and the formed angle is called a flat angle.
3. Rotate around the endpoint until the ending edge and the starting edge overlap again, and the angle formed is called fillet.
4. Degrees, minutes and seconds are commonly used units of angle measurement.
Divide a fillet into 360 equal parts, each equal part is an angle of one degree, and record it as1; Divide the angle of 1 degree into 60 equal parts, each part is called an angle of 1 minute, and it is recorded as1'; Divide the angle of 1 into 60 equal parts, and each part is called 1 sec, and it is recorded as 1 ".
The second volume of the first day of junior high school mathematics knowledge points
1. Know the triangle, know the meaning of the triangle, know the sides, internal angles and vertices of the triangle, and express the triangle in symbolic language.
2. Experience the practical activities of measuring the side length of a triangle and understand the unequal relationship among the three sides of the triangle.
3. Know how to judge whether three line segments can form a triangle, and use it to solve related problems.
4. The interior angle theorem of triangle can be deduced from the properties of parallel lines.
5. Some simple practical problems can be solved by applying the triangle interior angle sum theorem.
Second, the main points
Theorem of sum of interior angles of triangle;
In order to understand the concept of triangle, three bars can be expressed in symbolic language.
Third, difficulties.
The reasoning process of triangle interior angle sum theorem;
Identify all triangles without repetition or omission in specific graphics;
Judging whether three line segments can form a triangle by the unequal relationship of three sides of a triangle.
Fourth, the knowledge framework.
Verb (abbreviation of verb) summary of knowledge points and concepts
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. Classification of triangles
3. Trilateral relationship of triangle: the sum of any two sides of triangle is greater than the third side, and the difference between any two sides is less than the third side.
4. 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.
5. midline: in a triangle, the line segment connecting the vertex and the midpoint of its opposite side is called the midline of the triangle.
6. Angular bisector: The bisector of the inner angle of a triangle intersects the opposite side of this angle, and the line segment between the intersection of the vertex and this angle is called the angular bisector of the triangle.
7. Significance and practice of high line, middle line and angle bisector.
8. Stability of triangle: The shape of triangle is fixed, and this property of triangle is called stability of triangle.
9. Theorem of the sum of interior angles of triangle: the sum of three interior angles of triangle is equal to 180.
It is inferred that the two acute angles of 1 right triangle are complementary;
Inference 2: One outer angle of a triangle is equal to the sum of two non-adjacent inner angles;
Inference 3: One outer angle of a triangle is larger than any inner angle that is not adjacent to it;
Knowledge points of mathematics in the first semester
Intersecting line and parallel line
First, the knowledge network structure
Second, the main points of knowledge
1. In the same plane, there are two kinds of positional relationships between two straight lines: intersecting and parallel, and verticality is a special case of intersection.
2. On the same plane, two disjoint straight lines are called parallel lines. If two straight lines have only one common point, they are said to intersect; If two straight lines have no common point, they are said to be parallel.
3. Among the four angles formed by the intersection of two straight lines, two angles with a common vertex and a common edge are
The properties of adjacent complementary angles: complementary adjacent complementary angles. As shown in figure 1, they are complementary angles,
Fill the corner with neighbors. += 180 ; += 180 ; += 180 ;
+= 180 。
4. Among the four corners formed by the intersection of two straight lines, two sides of one corner are opposite extension lines of two sides of the other corner, so the two corners are opposite. The nature of antipodal angle: antipodal angle is equal. As shown in figure 1, and they are opposite to each other. =;
=。
5. If one of the angles formed by the intersection of two straight lines is a right angle or 90, the two straight lines are said to be perpendicular to each other.
One of them is called the perpendicular of the other. As shown in Figure 2, when = 90, ⊥.
Nature of vertical line:
Property 1: There is one and only one straight line perpendicular to the known straight line.
Property 2: Of all the line segments connecting a point outside the straight line and a point on the straight line, the vertical line segment is the shortest.
Property 3: As shown in Figure 2, when a ⊥ b = = = 90.
Distance from point to straight line: The length from a point outside a straight line to the vertical section of this straight line is called the distance from point to straight line.
6. The basic characteristics of congruent angle, internal dislocation angle and ipsilateral internal angle:
(1) is on the same side of two straight lines (cut lines) and the same side of the third straight line (cut lines), so that
These two angles are called isosceles angles. In Figure 3, * * * has a pair of isosceles angles; And is an isosceles angle;
And are at the same angle; And are at the same angle; And it's the same angle.
(2) Between two straight lines (secant) and on both sides of the third straight line (secant), such two angles are called inscribed angles. In figure 3; * * has a pair of inner corners; Is the inner corner; And is an inner corner.
(3) Between two straight lines (intersecting lines), both are on the same side of the third straight line (intersecting line), and such two angles are called ipsilateral inner angles. In figure 3; * * has a pair of inner corners on the same side; And are internal angles on the same side; And it is the same inner angle.
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