Ә.Н.Шыныбеков. Геометрия 7-сынып, 2012
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Ә.Н.Шыныбеков
Геометрия
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Ә.Н.Шыныбеков. Геометрия 7-сынып, 2012
Preparing book pages
1
Entries
57
Foreword
Other
Page 4
Axiomatic method of constructing geometry
Theory
Page 6
Chapter I. Basic concepts and axioms of plane geometry
Theory
Page 8
1. Point, line and segment
Theory
Page 8
1.1. Point and line
Theory
Page 8
1.2. Segment
Theory
Page 9
Problems
Problem
Page 12
2. Half-plane, ray and angle
Theory
Page 14
2.1. Half-plane
Theory
Page 14
2.2. Ray
Theory
Page 15
2.3. Angle
Theory
Page 16
2.4. Measuring and constructing segments and angles
Theory
Page 18
2.5. Axioms and theorems
Theory
Page 19
Problems
Problem
Page 21
3. Triangles
Theory
Page 24
3.1. Triangle
Theory
Page 24
3.2. Existence of a triangle congruent to a given triangle
Theory
Page 25
3.3. Parallel lines
Theory
Page 26
Problems
Problem
Page 27
4. Adjacent and vertical angles
Theory
Page 29
4.1. Adjacent and vertical angles
Theory
Page 29
4.2. Perpendicular lines
Theory
Page 30
4.3. Angle bisector
Theory
Page 32
4.4. Proof by contradiction
Theory
Page 32
Problems
Problem
Page 34
Chapter II. Triangle congruence criteria and their consequences
Theory
Page 37
1. Triangle congruence criteria
Theory
Page 37
1.1. First triangle congruence criterion
Theory
Page 37
1.2. Second triangle congruence criterion
Theory
Page 37
Problems
Problem
Page 39
1.3. Altitude, angle bisector and median of a triangle
Theory
Page 42
1.4. Concept of a converse theorem
Theory
Page 44
1.5. Third triangle congruence criterion
Theory
Page 46
Problems
Problem
Page 48
2. Criteria for parallel lines
Theory
Page 51
2.1. Angles formed by two lines and a transversal
Theory
Page 51
2.2. Sum of the interior angles of a triangle
Theory
Page 53
2.3. Right triangle
Theory
Page 54
Problems
Problem
Page 58
3. Relations between the sides and angles of a triangle
Theory
Page 62
3.1. Relations between the sides and angles of a triangle
Theory
Page 62
3.2. Triangle inequality
Theory
Page 63
Problems
Problem
Page 64
Chapter III. Circle and construction problems
Theory
Page 66
1. Circle
Theory
Page 66
1.1. Circle
Theory
Page 66
1.2. Circumcircle of a triangle
Theory
Page 67
1.3. Incircle of a triangle
Theory
Page 68
Problems
Problem
Page 69
2. Geometric construction problems
Theory
Page 71
2.1. Basic construction problems
Theory
Page 71
2.2. Constructing a triangle from three elements
Theory
Page 74
2.3. Construction problems
Theory
Page 75
Problems
Problem
Page 78
More difficult problems
Problem
Page 81
Appendices
Other
Page 85
Answers
Answer
Page 89
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