Ә.Н.Шыныбеков. Геометрия 8-сынып, 2012
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Ә.Н.Шыныбеков
Геометрия
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Ә.Н.Шыныбеков. Геометрия 8-сынып, 2012
Preparing book pages
1
Entries
72
Review of Grade 7 material
Problem
Page 4
Problems
Problem
Page 8
Chapter I. Quadrilaterals
Theory
Page 11
1. Polygons
Theory
Page 11
1.1. Concept of a polygon
Theory
Page 11
1.2. Convex polygons. Quadrilaterals
Theory
Page 12
Problems
Problem
Page 15
2. Parallelogram and its properties
Theory
Page 17
2.1. Properties of a parallelogram
Theory
Page 17
2.2. Criteria for a parallelogram
Theory
Page 18
Problems
Problem
Page 19
3. Rectangle, rhombus, square and their properties
Theory
Page 22
3.1. Rectangle
Theory
Page 22
3.2. Rhombus
Theory
Page 23
3.3. Square
Theory
Page 24
Problems
Problem
Page 25
4. Constructing quadrilaterals from their elements
Theory
Page 28
Problems
Problem
Page 32
5. Thales' theorem. Midline of a triangle
Theory
Page 33
5.1. Thales' theorem
Theory
Page 33
5.2. Midline of a triangle
Theory
Page 35
Problems
Problem
Page 35
6. Trapezoid and its properties
Theory
Page 37
Problems
Problem
Page 39
7. Remarkable points of a triangle. Circumcircle and incircle
Theory
Page 42
Problems
Problem
Page 46
8. Cyclic and tangential quadrilaterals
Theory
Page 49
Problems
Problem
Page 53
Chapter II. Pythagorean theorem
Theory
Page 56
1. Theorem on proportional segments. Pythagorean theorem
Theory
Page 56
1.1. Proportional segments
Theory
Page 56
1.2. Cosine of an acute angle
Theory
Page 58
1.3. Pythagorean theorem
Theory
Page 59
Problems
Problem
Page 61
2. Sine, tangent and cotangent of an acute angle
Theory
Page 64
2.1. Definitions of sine, tangent and cotangent of an acute angle
Theory
Page 64
2.2. Values of sine, cosine, tangent and cotangent of selected angles
Theory
Page 66
2.3. Trigonometric functions and finding their values
Theory
Page 67
Problems
Problem
Page 68
3. Metric relations in triangles
Theory
Page 72
Problems
Problem
Page 77
Chapter III. Areas of quadrilaterals
Theory
Page 79
1. Area of a rectangle
Theory
Page 79
1.1. Concept of the area of plane figures
Theory
Page 79
1.2. Area of a rectangle
Theory
Page 80
Problems
Problem
Page 82
2. Areas of a parallelogram, triangle and trapezoid
Theory
Page 84
2.1. Area of a parallelogram
Theory
Page 84
2.2. Area of a triangle
Theory
Page 85
2.3. Area of a trapezoid
Theory
Page 87
Problems
Problem
Page 88
Chapter IV. Rectangular coordinate system in the plane
Theory
Page 93
1. Cartesian coordinates of points in the plane. Distance between two points
Theory
Page 93
1.1. Rectangular Cartesian coordinate system
Theory
Page 93
1.2. Distance between two points
Theory
Page 94
1.3. Dividing a segment in a given ratio. Coordinates of the midpoint
Theory
Page 95
Problems
Problem
Page 98
2. Equations of a line and a circle
Theory
Page 101
2.1. Concept of an equation of a figure. Equation of a line
Theory
Page 101
2.2. Equation of a circle
Theory
Page 103
3. Equations of an ellipse, hyperbola and parabola
Theory
Page 105
3.1. Equation of an ellipse
Theory
Page 105
3.2. Equation of a hyperbola
Theory
Page 106
3.3. Equation of a parabola
Theory
Page 107
Problems
Problem
Page 108
4. Trigonometric functions of angles from 0° to 180°
Theory
Page 112
4.1. Sine, cosine and tangent of angles from 0° to 180°
Theory
Page 112
4.2. Reduction formulas
Theory
Page 113
Problems
Problem
Page 115
Additional advanced-level problems
Problem
Page 116
Subject index
Other
Page 120
Answers to problems
Answer
Page 121
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