In the senior high school entrance examination, geometry problem solving and geometry proof are hot topics. Definitions and theorems are often used in the process of solving, and the specific process needs to be expressed in symbolic language. Therefore, students must master the geometric representation of each theorem. The following is the symbolic language of all geometric theorems involved in the seventh grade of junior high school:
Contents of "Graphics and Geometry" in Junior Middle School Mathematics (subject to the textbook published by Beijing Normal University)
The first volume of the seventh grade
1. Basic fact: There is only one straight line after two o'clock. (Two points define a straight line)
2. Basic fact: The line segment between two points is the shortest.
3. The nature of complementary angle: the complementary angle of the same angle or equal angle is equal.
Geometric language: ≈a+∠b = 180, ∠ A+∠ C = 180 ∴∠ B = ∠ C (complementary angles of the same angle are equal).
∠∠a+∠b = 180，∠ C+∠C +∠D = 180，∠a =∠c∴∠b =∞。
4. The nature of complementary angle: the same angle or the complementary angle of the same angle is equal.
Geometric language: ∵∠ A+∠ B = 90, ∠ A+∠a+∠c = 90°∴∠b =∠c ∠ C (complementary angles of the same angle are equal).
∠∠ A+∠ B = 90, ∠ C+∠C+∠D = 90°, ∠ A = ∠ C ∠ B = ∠ D (complementary angles of equal angles are equal).
The second volume of the seventh grade
5. The nature of the vertex angle: the vertex angle is equal.
6. There is one and only one straight line perpendicular to the known straight line.
7. Of all the line segments connecting points outside the straight line and points on the straight line, the vertical line segment is the shortest. (The vertical segment is the shortest)
8. (Basic fact) Parallelism axiom: After a point outside a straight line, there is one and only one straight line parallel to this straight line.
9. If two straight lines are parallel to the third straight line, then the two straight lines are also parallel to each other.
Geometric languages: ∫a∨b, A ∨ C ∴ B ∨ C.
10. Determination method of parallelism of two straight lines: geometric language: as shown in the figure.
(1) At the same angle, two straight lines are parallel. ∫≈ 1 =∠2 ∴a∥b
(2) The internal dislocation angles are equal and the two straight lines are parallel. ∠∠3 =∠4 ∴a∥b
(3) The internal angles on the same side are complementary and the two straight lines are parallel. ∫≈5+≈6 = 180 ∴a∥b
1 1. Properties of parallel lines: geometric language: as shown in the figure.
(1) Two straight lines are parallel with the same included angle. ∫a∨b ∴∠ 1=∠2
(2) The two straight lines are parallel and the internal dislocation angles are equal. ∫a∨b ∴∠3=∠4
(3) Two straight lines are parallel and complementary. ∫a∨b ∴∠5+∠6= 180
12, translated by:
(1) Moving the whole graph along a straight line will produce a new graph with the same shape and size as the original graph.
(2) Every point in the new graph is obtained by moving a point in the original graph. These two points are corresponding points, and the line segments connecting each group of corresponding points are parallel and equal.
13. Trilateral relation theorem of triangle: the sum of two sides of triangle is greater than the third side.
14. Inference of triangle trilateral relationship: the difference between any two sides in a triangle is smaller than the third side.
15, the theorem of the sum of the internal angles of a triangle: the sum of the three internal angles of a triangle is equal to 180.
16, one outer angle of a triangle is equal to the sum of two non-adjacent inner angles.
17, the outer angle of the triangle is larger than any inner angle that is not adjacent to it.
18, the sum of polygon internal angles: the sum of n polygon internal angles is equal to (n-2) × 180.
19, the sum of the outer angles of the polygon is equal to 360.
Hope to adopt, O(∩_∩)O Thank you!