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Grade 9
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Geometry
Geometry · Grade 9
34/34 weeks ready · B. Xaydarov, E. Sariqov, A. Qo‘chqorov. Geometry, Grade 9 (textbook for general secondary schools), revised 4th edition. Huquq va Jamiyat Publishing, Tashkent, 2019
Review (Grades 5–8)
1
Review of Grades 5–8: triangles and quadrilaterals
1. Triangles and quadrilaterals
Quiz (8)
Homework
2
The Pythagorean theorem and its applications
2. The Pythagorean theorem and its applications
Quiz (8)
Homework
3
Calculating perimeter and area
3. Problems on the perimeter and area of geometric figures
Quiz (8)
Homework
4
Plane geometry in solids; project work
4. 3D geometry: plane-geometry problems in solids
5. Guidelines for doing a project
Quiz (8)
Homework
Chapter I
Geometric transformations and similarity
5
Similarity of polygons and triangles
6. Similarity of polygons
7. Similar triangles and their properties
Quiz (8)
Homework
6
The AA and SAS similarity tests
8. The first test for similar triangles
9. The second test for similar triangles
Quiz (8)
Homework
7
The SSS test and right triangles
10. The third test for similar triangles
11. Tests for similar right triangles
Quiz (8)
Homework
8
Applications of similarity and review
12. Using similarity tests in proof problems
13. Practical exercise and application
14. Test your knowledge
Quiz (10)
Homework
9
Motion, translation and symmetry about a line
15. Geometric transformations of the plane. Motion and translation
16. Symmetry about a line
Quiz (8)
Homework
10
Central symmetry and rotation
17. Central symmetry and rotation
Quiz (8)
Homework
11
Similarity of figures; properties of similar polygons
18. Similarity of geometric figures
19. Properties of similar polygons
Quiz (8)
Homework
12
Homothety and constructing similar polygons
20. Homothety and similarity
21. Constructing similar polygons
Quiz (8)
Homework
13
Practical applications of similarity
22. Practical exercise and application
Quiz (8)
Homework
14
Mixed problems and Chapter I review
23. Problem solving
24. Test your knowledge
Quiz (10)
Homework
Chapter II
Relations between the sides and angles of a triangle
15
Sine, cosine, tangent and cotangent of an angle
25. Sine, cosine, tangent and cotangent of an angle from 0° to 180°
Quiz (8)
Homework
16
Problems with trigonometry and the area of a triangle
26. Problem solving
27. Area of a triangle using the sine of an angle
Quiz (8)
Homework
17
The law of sines
28. The law of sines
Quiz (8)
Homework
18
The law of cosines
29. The law of cosines
Quiz (8)
Homework
19
Applications of the theorems; dot product
30. Some applications of the laws of sines and cosines
31. The angle between two vectors and their dot product
Quiz (8)
Homework
20
Solving triangles; mixed problems
32. Solving triangles
33. Problem solving
Quiz (8)
Homework
21
Practical applications and Chapter II review
34. Practical exercise and application
35. Test your knowledge
Quiz (10)
Homework
Chapter III
Circumference and area of a circle
22
Inscribed and circumscribed polygons
36. A polygon inscribed in a circle
37. A polygon circumscribed about a circle
Quiz (8)
Homework
23
Regular polygons
38. Regular polygons
Quiz (8)
Homework
24
Circles inscribed in and circumscribed about regular polygons
39. Circles inscribed in and circumscribed about a regular polygon
40. How the side of a regular polygon relates to the radii of its circumscribed and inscribed circles
Quiz (8)
Homework
25
Review and the circumference of a circle
41. Test your knowledge
42. Circumference of a circle
Quiz (8)
Homework
26
Arc length and radian measure
43. Length of an arc. The radian measure of an angle
Quiz (8)
Homework
27
Area of a disc and its parts
44. Area of a circle
45. Areas of parts of a circle
Quiz (8)
Homework
28
Practice and the Chapter III test
46. Practical exercise and application
47. Test your knowledge
Quiz (8)
Homework
Chapter IV
Metric relations in a triangle and a circle
29
Projections of segments
48. Projections of segments and proportionality
Quiz (8)
Homework
30
Properties of proportional segments
49. Properties of proportional segments
Quiz (8)
Homework
31
Proportional segments in a right triangle
50. Proportional segments in a right triangle
51. Constructing the mean proportional of two given segments
Quiz (8)
Homework
32
Proportional segments in a circle
52. Proportional segments in a circle
Quiz (8)
Homework
33
Practice and the Chapter IV test
53. Practical exercise and application
54. Test your knowledge
Quiz (8)
Homework
34
Final review
55. Final control test
Quiz (8)
Homework
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