И.Бекбоев. Геометрия 9-сынып, 2009

Chapter I. Vectors in the plane

§1. Concept of a vector. Collinear vectors. Equal vectors

§2. Operations on vectors

2.1. Addition of vectors

2.2. Subtraction of vectors

2.3. Multiplication of a vector by a scalar

2.4. Coordinates of a vector

§3. Dot product of two vectors

3.1. Angle between two vectors

3.2. Dot product of two vectors

Historical notes

Chapter II. Transformations of figures in the plane

§4. Transformation of the plane. Isometry and its properties

4.1. Transformation of the plane

4.2. Isometry and its properties

4.3. Axial and central symmetries

4.4. Rotation

§5. Similarity transformation. Similar figures. Homothety

5.1. Similarity transformation. Similar figures

5.2. Homothety

5.3. Properties of similarity transformations

§6. Triangle congruence criteria

6.1. Triangle similarity criteria

6.2. Similarity criteria for right triangles

§7. Inscribed angle and its properties

§8. Proportionality of chords and intersecting segments of a circle

Historical notes

Chapter III. Polygons

§9. Law of cosines. Law of sines

§10. Applying the laws of cosines and sines to solve triangles

§11. Polygonal line. Polygon and its types

11.1. Polygonal line

11.2. Polygons

11.3. Sum of the angles of a convex polygon

11.4. Regular polygons

§12. Inscribed and circumscribed polygons

12.1. Inscribed and circumscribed quadrilaterals

12.2. Inscribed and circumscribed regular polygons

§13. Circumference. The number π

13.1. Circumference. Determination using the perimeters of inscribed and circumscribed regular polygons

13.2. The number π

13.3. Arc length

§14. Area of a polygon

14.1. Calculating the area of an arbitrary polygon

14.2. Areas of circumscribed and inscribed polygons

§15. Area of a disk and its parts

Historical notes

Chapter IV. Elements of solid geometry

§16. Relative positions of two lines, a line and a plane, and two planes in space

§17. Parallelepiped. Prism. Pyramid

§18. Cylinder. Cone. Sphere

Historical notes

Subject index

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