Parallel straight lines option 2 part 1. What is the manual

8th ed., Rev. and add. - M .: 2015 .-- 126s. M .: 2009. - 126s.

The manual is a necessary addition to school geometry textbooks for grade 7, recommended by the Ministry of Education and Science Russian Federation and included in the Federal List of Textbooks. The manual contains thematic tests, which are structured like measuring materials for the Basic State Exam in Mathematics. The tests are focused on the textbook by L. S. Atanasyan et al. “Geometry. 7-9 grades ”, but can be used by teachers working on other textbooks. All tests are compiled in 4 versions. The manual is intended for teachers of mathematics; it can also be used by 7th grade students to prepare for control works and credits, as well as members of the certification commissions for the certification of schools.

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Format: pdf (2009, 126s.)

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CONTENT
Introduction 7
Student Instructions 10
Topic I. Initial geometric information 11
Option 1 11
Part 1 11
Part 2 12
Part 3 14
Option II 15
Part 1 15
Part 2 16
Part 3 18
Option III 19
Part 1 19
Part 2 20
Part 3 22
Option IV 23
Part 1 23
Part 2 24
Part 3 26
Topic II. Triangles 27
Option 1 27
Part 1 27
Part 2 29
Part 3 31
Option II 32
Part 1 32
Part 2 34
Part 3 35
Option III 36
Part 1 36
Part 2 38
Part 3 39
Option IV 40
Part 1 40
Part 2 42
Part 3 44
Topic III. Parallel lines 45
Option 1 45
Part 1 45
Part 2 47
Part 3 49
Option II 50
Part 1 50
Part 2 52
Part 3 54
Option III 55
Part 1 55
Part 2 57
Part 3 59
Option IV 60
Part 1 60
Part 2 62
Part 3 64
Topic IV. Relationship between angles and sides of a triangle 65
Option 1 65
Part 1 65
Part 2 67
Part 3 69
Option II 70
Part 1 70
Part 2 72
Part 3 73
Option III 74
Part 1 74
Part 2 76
Part 3 77
Option IV 78
Part 1 78
Part 2 80
Part 3 81
Topic V. Right triangle... Constructing a Triangle Using Three Elements 82
Option I 82
Part 1 82
Part 2 85
Part 3 86
Option II 87
Part 1 87
Part 2 89
Part 3 90
Option III 91
Part 1 91
Part 2 94
Part 3 95
Option IV 96
Part 1 96
Part 2 99
Part 3 100
Answers and guidelines 101
Sample Form for Student Answer 102
Topic I. Initial geometric information 103
Option I 103
Option II 104
Option III 105
Option IV 106
Topic II. Triangles 107
Option I 107
Option II 108
Option III 109
Option IV 110
Topic III. Parallel lines 111
Option I 111
Option II 112
Option III 113
Option IV 114
Topic IV. Relationship Between Angles and Sides of a Triangle 115
Option I 115
Option II 117
Option III 118
Option IV 120
Topic V. Rectangular triangle. Constructing a Triangle Using Three Elements 122
Option I 122
Option II 123
Option III 124
Option IV 125

Tasks in planimetry are included both in the number of USE tasks in mathematics and in the number of tasks of the OGE (GIA-9) in mathematics.
The best remedy to prepare students for the Unified State Exam and the OGE is teaching mathematics, including geometry, a good teacher from a good textbook. One of such textbooks is the textbook of L.S. Atanasyan and others. “Geometry. 7-9 grades ". Unfortunately, there are not enough tasks similar to the geometric tasks proposed in part 1 of the OGE and part B of the exam in mathematics.
This manual is intended both to check the level of learning of students in geometry, and to prepare students for the upcoming forms of certification.
Therefore, the thematic tests developed in the manual can be offered along with tests and other means of diagnosing the level of student learning and as a final work on the topic (without offering tests in this case) .The manual contains tasks with a choice of answer (Part 1), tasks with a short the answer (Part 2). It also contains one problem (Part 3), to which you need to give a detailed answer. As tasks of level C, tasks of increased difficulty are proposed, similar to the tasks of the second part of the GIA in mathematics. Tasks of this kind are usually suggested as the last task of control works.
The proposed tests are compiled in four versions for each topic of the 7th grade geometry course in relation to the geometry textbook for students in grades 7-9 authors L.S. Atanasyan and others, although with some adjustment, these tests can also be offered to students studying according to A.V. Pogorelova and I.F. Sharygin.
The duration of these tests is 35-40 minutes. But if the teacher thinks that the problem from part C does not need to be included in the test, then the time for the test can be reduced to 20-25 minutes.

Control on the topics: "Basic geometric information", "Triangle and circle", "Parallel lines", "Triangle. The relationship between angles and sides"

Test number 1 on the topic: "Straight on a plane. Angles"

Option I.

a) point C, lying on the beam BA;
b) point D, not lying on line AB;
c) point E, not lying on line AB, and draw a line through this point, + intersecting AB.

2. Solve the problem.
a) One of the angles formed at the intersection of two straight lines is 123 0. Find the rest of the corners.
b) One of the adjacent corners is five times the size of the other. Find these corners.


a) MN, if CD \u003d 6 cm, CN \u003d 4 cm, CM \u003d 2 cm.
b) CN, if CM \u003d 3 cm, MD \u003d 7 cm, ND \u003d 1 cm.

4. The bisector of the angle and the straight line intersecting the sides of the angle form an angle α. Find the original angle if you know that this line is perpendicular to one of the sides.

5. The COD angle \u003d 124 0, the OE beam is the bisector of the COD angle, and the OF beam divides one of the resulting angles in a ratio of 3: 1. Find the resulting corners.

Option II.
1. Draw line AB and mark the points:
a) point C lying on the segment AB.
b) point F, not lying on line AB.
c) point E, not lying on line AB, and draw a line through this point that intersects AB.

2. Solve the problem.
a) One of the angles formed at the intersection of two straight lines is 144 0. Find the rest of the corners.
b) One of the adjacent corners is 9 times smaller than the other. Find these corners.

3. On the segment CD, points M and N are sequentially marked. Find the length of the segment:
a) MN, if CD \u003d 8 cm, CN \u003d 5 cm, CM \u003d 1 cm.
b) CN, if CM \u003d 4 cm, MD \u003d 9 cm, ND \u003d 2 cm.

4. A straight line is perpendicular to one of the sides of the corner and forms an angle α with a straight line drawn from the corner apex. Find the starting corner.

5. Angle COD \u003d 144 0, ray OE and OF divide this angle by three. The bisector OM is drawn in the EOF angle. Find the angles COM, MOD, EOM, MOF, COF.

Examination number 2 on the topic: "Triangles"

Option I.

a) AH - median.
b) BM is the median.
c) AH - height.
d) BM - bisector.
e) $ \\ bigtriangleup ABC $ - isosceles.

2. The perimeter of $ \\ bigtriangleup ABC $ is 12 cm, AC side \u003d 5cm, BC \u003d 4cm. It is known that AB \u003d CD, ∠DCA \u003d 30 °, ∠BAH \u003d 150 °.
a) Prove that $ \\ bigtriangleup ABC \u003d \\ bigtriangleup DCA $.


3. In $ \\ bigtriangleup ABC $ AB \u003d AC, AH is the bisector, ∠ABC \u003d 57 °. Find the corners $ \\ bigtriangleup ABC $.

4. The chords AC and BE are drawn in a circle centered at point O, so that ∠AOB \u003d ∠COE.
Prove: a) AC \u003d BE; b) AE - the diameter of the circle.

5. $ \\ bigtriangleup ABC $ isosceles (BC \u003d AC). Point D is taken inside the triangle so that BD \u003d AD, ∠ADB \u003d 120 °, ∠A \u003d 60 °. Find ∠BDC and ∠DAC.

Option II.
1. Using the picture, select the correct answer:
a) AH is a bisector.
b) BM is the median.
c) AH - height.
d) BM - bisector.
e) $ \\ bigtriangleup ABC $ - acute-angled.

2. The perimeter of $ \\ bigtriangleup ABC $ is 18 cm, AC side \u003d 6cm, BC \u003d 5cm. It is known that AB \u003d CD, ∠DCA \u003d 60 °, ∠BAH \u003d 120 °.
a) Prove that $ \\ bigtriangleup ABC $ \u003d $ \\ bigtriangleup DCA $.
b) Find the lengths of the sides $ \\ bigtriangleup DCA $.

3. In $ \\ bigtriangleup ABC, $ AB \u003d AC, AH is the height, ∠ABC \u003d 38 °. Find the corners $ \\ bigtriangleup ABC $.

4. Chords AF and BM are drawn in a circle centered at point O so that ∠AOF \u003d ∠BOM.
Prove: a) AB \u003d FM; b) AM is the diameter of the circle.

5. $ \\ bigtriangleup ABC $ isosceles (BC \u003d AC). Point D is taken inside the triangle, so that BD \u003d AD, ∠ADB \u003d 120 ° ,; ∠A \u003d 60 °. Find ∠BDC and ∠DAC.

Examination number 3 on the topic: "Parallel lines"

Option I.

2. In the figure ∠1 \u003d 126 °, and || b. Find ∠2, ∠3, ∠4.

3. Lines AB and CD meet at point O. Prove that if AD || BC and OD \u003d CO, then $ \\ bigtriangleup AOD \u003d \\ bigtriangleup COB $.

4. $ \\ bigtriangleup ABC $ isosceles, МР || BC, MP || KH, ∠B \u003d 70 °, AM: MB \u003d 1: 2, MK: KB \u003d 1: 3, AB \u003d 6 cm. Find: ∠A , ∠AKH, ∠KHA, HC.

5. $ \\ bigtriangleup ABC $ isosceles (AB \u003d AC), AH - height, ∠C \u003d 52 ° ∠ MBA \u003d 76 °. Prove that MB || AC.

Option II.
1. Using the picture, prove that a || b and c || d.

2. In the figure ∠1 \u003d 132 °, and || b. Find ∠2, ∠3, ∠4.

3. Lines AB and CD meet at point O. Prove that if AC || BD and AO \u003d OB, then $ \\ bigtriangleup AOC \u003d \\ bigtriangleup ODB $.

4. $ \\ bigtriangleup ABC $ isosceles, МР || BC, MP || KH, ∠B \u003d 80 °, AM: MB \u003d 1: 3, MK: KB \u003d 1: 5, AB \u003d 8cm. Find: ∠A, ∠AKH, ∠KHA, HC.

5. Given $ \\ bigtriangleup ABC $, AH - height, ∠B \u003d 38 ° ∠MBA \u003d 104 °. Prove that MB || AC.

Test number 4 on the topic: "Relationship between the angles and sides of the triangle"

Option I.
a) $ \\ bigtriangleup ABC $ - isosceles;
b) $ \\ bigtriangleup ABC $ - obtuse;
c) ∠C \u003d 80 °
d) ∠2 - external to $ \\ bigtriangleup ABC $.

2. In isosceles $ \\ bigtriangleup ABC $ with base АС, АН - height, ∠B \u003d 45 °. Find all possible inner corners $ \\ bigtriangleup ABC $.

3. In $ \\ bigtriangleup ABC, $ ∠B is more than ∠A by 30 °, and ∠C is $ 1 \\ frac (1) (3) $ times greater than ∠A. Find the corners $ \\ bigtriangleup ABC $.

4. Using the data in the figure, find AB.

5. In equilateral $ \\ bigtriangleup ABC $ the height AH is drawn. Point M is marked on the side AB. Through this point, a perpendicular is drawn to the side AC, which intersects it at point N. AH and MN intersect at point O. Find the angles of the quadrilateral MBHO.

Option II.
1. Using the picture, select the correct statements:
a) BC \u003d AC;
b) $ \\ bigtriangleup ABC $ - rectangular;
c) ∠A \u003d 67 °
d) external angle to ∠A \u003d 153 °.

2. In isosceles $ \\ bigtriangleup ABC $ with base АС, АН - height, ∠B \u003d 50 °. Find all possible interior angles of $ \\ bigtriangleup ABC $.

3. In $ \\ bigtriangleup ABC, $ ∠B is 12 ° more than ∠A, and ∠C is 2 times more than A. Find the corners $ \\ bigtriangleup ABC $.

4. Using the data in the figure, find BC.

5. In equilateral $ \\ bigtriangleup ABC $ the height AH is drawn. Point M is marked on the side AB. Through this point, a straight line is drawn that intersects the side AC at point N. AH and MN intersect at point O. ∠MNA \u003d 60 °. Find the corners of the MBHO quadrilateral.

Examination work No. 5 (final)

Option I.

2. In equilateral $ \\ bigtriangleup ABC $ on the bisector ВН, the point О is taken so that ON⊥BC; OM⊥AB (N∈BC, M∈AB). Prove that $ \\ bigtriangleup AOM \u003d \\ bigtriangleup NOC $. Find the corners of these triangles.

3. In a circle centered at point O, chords AB and CD meet at point N. ∠CNB \u003d 150 °; CD⊥OB; CO⊥AB. Find ∠COB.

4. In $ \\ bigtriangleup ABC $ AB \u003d BC, points K and E are marked on sides AB and AC so that KE || BC, KH is the bisector of ∠BKE; ∠BKH \u003d 32 °. Find the corners $ \\ bigtriangleup ABC $.

5. Prove that if two line segments are equal and the intersection point is divided in the same ratio, then the line segments connecting the ends of these segments are parallel.

Option II.
1. Using the picture, find the isosceles triangles:

2. In equilateral $ \\ bigtriangleup ABC $ at the height ВН the point О is taken so that ON⊥BC; OM⊥AB (N∈BC, M∈AB). Prove that $ \\ bigtriangleup MOB \u003d \\ bigtriangleup NOB $. Find the corners $ \\ bigtriangleup ABC $.

3. In a circle centered at point O, the chords AB and CD meet at point N. ∠AND \u003d 120 °; CD⊥OB; CO⊥AB. Find ∠COB.

4. In $ \\ bigtriangleup ABC $ AB \u003d BC, points M and N are marked on sides AB and AC so that MN || BC, NH is the bisector of ∠MNC; ∠HNC \u003d 53 °. Find the corners $ \\ bigtriangleup ABC $.

5. Prove that if two line segments intersect in the middle, then the line segments connecting the ends of these segments are parallel.


Option I.
1.3 and 4.
2.67.5 °; 22.5 °; 45 °; 90 °; 90 °; 45 °.
3.45 °; 75 °; 60 °.
4. AB \u003d 8.
5.150 °; 60 °; 90 °; 60 °.

Option II.
1.1 and 3.
2.40 °; 25 °; 65 °; 90 °; 90 °; 50 °.
3.42 °; 84 °; 54 °.
4. BC \u003d 8.
5.120 °; 60 °; 90 °; 60 °.

Answers to test number 5 (final)
Option I.
1.a, c.
2.60 °; 30 °; 90 °.
3.30 °.
4.32 °; 32 °; 116 °.

Option II.
1.a, c.
2.30 °; 30 °; 120 °.
3.60 °.
4.32 °; 74 °; 74 °.

The manual is intended to test the level of learning of students in the geometry course of grade 7 and to prepare for passing the exam mathematics. It contains thematic tests, which in structure resemble measuring materials for the Unified State Exam in Mathematics. The tests are focused on the textbook of L.S. Atanasyan et al. "Geometry. Grades 7-9", but can be used by teachers working according to other textbooks. All tests are compiled in 4 versions.
The manual is intended for teachers of mathematics; it can also be used by 7th grade students to prepare for tests and tests, as well as members of attestation commissions for attestation of schools.

Examples.
In an isosceles triangle ABC with base AC, the segment BD is the height of the triangle. Then BD is also
a) the bisector of the triangle;
b) the median of the triangle;
c) a perpendicular drawn from point B to the straight line AC, as well as the median and bisector of the triangle;
d) median and bisector of the triangle.

The perimeter of an isosceles triangle is 41 cm, and the lateral side is 3.5 cm less than the base. Then the base of the triangle will be
a) 12 cm;
b) 16 cm;
c) 15.5 cm;
d) 12.5 cm.

If the triangle is isosceles, then
a) it is also equilateral;
b) any of its median is the bisector and height;
c) the angles at the base will be equal;
d) it is also rectangular.

CONTENT
Introduction 7
Student Instructions 10
Topic I. Initial geometric information 11
Option 1 11
Part 1 11
Part 2 12
Part 3 14
Option II 15
Part 1 15
Part 2 16
Part 3 18
Option III 19
Part 1 19
Part 2 20
Part 3 22
Option IV 23
Part 1 23
Part 2 24
Part 3 26
Topic II. Triangles 27
Option 1 27
Part 1 27
Part 2 29
Part 3 31
Option II 32
Part 1 32
Part 2 34
Part 3 35
Option III 36
Part 1 36
Part 2 38
Part 3 39
Option IV 40
Part 1 40
Part 2 42
Part 3 44
Topic III. Parallel lines 45
Option 1 45
Part 1 45
Part 2 47
Part 3 49
Option II 50
Part 1 50
Part 2 52
Part 3 54
Option III 55
Part 1 55
Part 2 57
Part 3 59
Option IV 60
Part 1 60
Part 2 62
Part 3 64
Topic IV. Relationship between angles and sides of a triangle 65
Option 1 65
Part 1 65
Part 2 67
Part 3 69
Option II 70
Part 1 70
Part 2 72
Part 3 73
Option III 74
Part 1 74
Part 2 76
Part 3 77
Option IV 78
Part 1 78
Part 2 80
Part 3 81
Topic V. Rectangular triangle. Constructing a Triangle Using Three Elements 82
Option 1 82
Part! 82
Part 2 85
Part 3 86
Option II 87
Part 1 87
Part 2 89
Part 3 90
Option III 91
Part 1 91
Part 2 94
Part 3 95
Option IV 96
Part 1 96
Part 2 99
Part 3 100
Answers and guidelines 101
Sample Form for Student Answer 101
Topic I. Initial geometric information 103
Option 1 103
Option II 104
Option III 105
Option IV 106
Topic II. Triangles 107
Option I 107
Option II 108
Option III 109
Option IV 110
Topic III. Parallel lines 111
Option I 111
Option II. 112
Option III 113
Option IV 114
Topic IV. Relationship Between Angles and Sides of a Triangle 115
Option I 115
Option II 117
Option III 118
Option IV 120
Topic V. Rectangular triangle. Constructing a Triangle Using Three Elements 122
Option I 122
Option II. 123
Option III 124
Option IV 125.


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Test work Parallel straight lines 7th grade (according to the textbook Atanasyan). The manual is addressed to parents who will be able to check the correctness of the solution, and, if necessary, help the children with their homework on geometry. The answers to the test are given at the end of the article.

Test work is designed for one lesson (45 minutes) and allows differentiated knowledge control, since the tasks are distributed over three difficulty levels A, B and C. Level AND meets mandatory software requirements, B - medium difficulty level, IN - for students with an increased interest in mathematics, as well as for use in classrooms, schools, gymnasiums and lyceums with in-depth study mathematics. For each level, there are two adjacent equivalent options.

Examination in geometry grade 7
"KA-3. PARALLEL LINE "

1. Examination in geometry grade 7. KA-3.

Option A1.
1. In this figure, ∠1 \u003d 82 °, ∠2 \u003d 119 °, ∠3 \u003d 82 °.
a) Find ∠4.

2. From points A to B, lying on one of the sides of a given acute angle, perpendiculars AC and BD are drawn to the second side of the corner.
a) Prove that AC || BD.
b) Find ∠ABD if ∠CAB \u003d 125 °.
3. Points D and E are marked on the sides AB and BC of triangle ABC, respectively. Prove that if ∠BDE \u003d ∠BAC then ∠BED \u003d ∠BCA.

Option A2
1. In this figure ∠1 \u003d 112 °, ∠2 \u003d 68 °, ∠3 \u003d 63 °.
a) Find ∠4.
b) How many angles equal to ∠4 are shown in the figure? Mark these corners.
2. From points C and D, lying on one of the sides of a given acute angle, perpendiculars to this side are drawn, intersecting the second side of the angle at points A and B, respectively.
a) Prove that AC || BD.
b) Find ∠CAB if ∠ABD \u003d 55 °.
3. Points D and E are marked on the sides AB and BC of triangle ABC, respectively. Prove that if ∠BED \u003d ∠BCA then ∠BDE \u003d ∠BAC.

2. Examination in geometry grade 7. KA-3. Options B1 and B2.


3. Examination in geometry grade 7. KA-3. Variants B1 and B2.


Test work Parallel straight lines 7th grade. ANSWERS

Option A1: 1-a) 61 °, 1-b) three more angles, 2-a) АС⟂СD, BD⟂CD ⇒ AC || BD, 2-b) 55 °.

Option A2: 1-a) 63 °, 1-b) three more angles, 2-a) AC⟂AB, BD⟂AB ⇒ AC || BD, 2-b) 125 °.

Option B1: 1-b) 64 °, 2-a) 38 °, 2-b) 102 °.

Option B2: 1-b) 26 °, 2-a) 25 °, 2-b) 119 °.

Option IN 1: 1) 158 °, 2-a) 50 °, 2-b) 40 °.

Variant B2: 1) 107 °, 2-a) 50 °, 2-b) 40 °.

A source : Ershova A.P., Goloborodko V.V., Ershova A.S. - Independent and test work in algebra and geometry for grade 7. 8th ed., Rev. and additional - M .: ILEKSA, - 2013.

Program for geometry saturated with a wide variety of topics. Students need to master a huge amount of material in a short period of time. Unsurprisingly, in seventh grade there are often serious knowledge gaps that snowball. The task of parents and a teacher is to timely identify and eliminate problems in the study of the material.

Student assistant

The elements geometry already familiar seventh grader on previous years of study, when mathematics included the basics of knowledge in two disciplines - algebra and geometry. But now items have reached a new, extremely high level of difficulty. High-quality educational literature is designed to help the student understand the nuances of the subject and reliably prepare for any test work - a textbook solution to the textbook "Geometry Grade 7 Tests Farkov to the textbook Atanasyan Exam".

What is the benefit

Reshebnik not only prompts the student to the correct answer, but also explains the solution algorithm, teaches the correct variant of recording the exercise. Briefly about the contents of the collection of tests:

  • Initial geometric information.
  • Triangles.
  • Parallel lines.
  • The relationship between the angles and sides of a triangle.
  • Right triangle.

Regular work with the manual will allow the student to master this complex subject and prepare reliably for tests in the classroom.

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