Шыныбеков Геометрия 9-кл1

Review of Grade 7–8 material

Problems

1.1. Concept of a vector

1.2. Equality of vectors

1.3. Properties of vector equality

2.1. Vector addition

2.2. Properties of vector addition

2.3. Difference of vectors

2.4. Decomposition of a vector along two intersecting directions

3.1. Multiplication of a vector by a scalar and its properties

3.2. Criterion for collinearity of vectors

4.1. Concept of the angle between vectors

4.2. Dot product of vectors

4.3. Some applications of vectors

5.1. Decomposition of any vector in terms of two non-collinear vectors

5.2. Coordinates of a vector in a rectangular coordinate system

5.3. Coordinates of a vector given by its endpoints. Position vector

6.1. Coordinate form of the dot product of vectors

6.2. Coordinate conditions for perpendicularity and collinearity of vectors. Determining the angle between vectors

Problems

7.1. Equations of a line. Direction and normal vectors of a line

7.2. Some applications of the coordinate method

8.1. Central symmetry

8.2. Axial symmetry

9.1. Rotation

9.2. Translation

10.1. Isometry and its properties

10.2. Superpositions and isometries

11.1. Concept of similarity transformation and its properties

11.2. Homothety

12. Triangle similarity criteria

13. Applications of similarity. Properties of triangle angle bisectors

14.1. Polygonal lines. Convex polygons

14.2. Regular polygons

14.3. Similarity of regular polygons

15. Cyclic and tangential quadrilaterals

16.1. Proportional segments in a circle

16.2. Metric relations in a right triangle

17.1. Law of cosines

17.2. Law of sines

18. Solving triangles

19. Applying trigonometry to solving triangles

20.1. Diameters and chords

20.2. Relative positions of two circles

21.1. Concept of the length of a curved line

21.2. Circumference

22.1. Area of a circle

22.2. Area of a sector and a segment

23. Axioms of solid geometry