Initial geometric information points straight line segments rays. Initial geometric information
Didactic material
For check theoretical knowledge for the 7th grade geometry course.
1. Mark the correct statements with a “+” sign and erroneous ones with a “-” sign.
1. Examples of geometric figures on a plane are a point, a straight line, a square, a cube, a ball.
2. Examples of geometric figures on a plane are a point, a straight line, a ray, a segment, a polygon.
3. Two lines either have only one common point or do not have common points.
4. Three straight lines can be drawn through any two points.
5. A segment is a part of a straight line.
6. A ray is a part of a straight line, consisting of all points of this straight line that lie on one side of a given point on it.
7. The beginning of the beam AB is point B.
8. Angle is a geometric figure consisting of a point and two rays emanating from this point.
9. Any corner can have multiple vertices.
10. The point of the segment that divides it in half is called the midpoint of the segment.
11. An undeveloped angle is always greater than a developed one.
12. An undeveloped angle is always less than a developed one.
13. The bisector of an angle is a ray emanating from the vertex of the angle, dividing the angle into two equal angles.
14. The length of a segment is the distance between any of its points.
15. Any point lying on a segment divides it into two parts.
16. If point B belongs to the segment AK, then AK \u003d AB - BK.
17. A developed angle has a degree measure of 90 0.
18. An angle is called right if it is equal to 60 0 .
19. An acute angle is always less than a right one.
20. Two angles that have one side in common and the other two are continuations of one another are called adjacent.
21. The sum of adjacent angles is 180 0 .
22. Amount vertical angles always 100 0 .
23. If two adjacent angles are equal, then they are right.
Initial geometric information.
2. Mark the correct statements with a "+" sign and erroneous ones with a "-" sign.
1. Two lines always have a common point.
2. A segment is a part of a straight line, consisting of all points of this straight line lying between two given points of it.
3. Angle is a geometric figure consisting of a point and three rays emanating from this point.
4. Geometric figures are called equal if all their sides are equal in pairs.
5. Geometric figures are called equal if they coincide when superimposed.
6. An angle is called deployed if both of its sides lie on the same straight line.
7. Any ray emanating from the vertex of an angle divides it into two equal angles.
8. The length of a segment is the distance between its ends.
9. The length of a segment is equal to the sum of the lengths of its parts into which it is divided by any of its points.
10. Units of measurement of angles - degrees.
11. An obtuse angle is always less than a right angle.
12. Two angles are called vertical. If the sides of one angle are extensions of the sides of another.
13. Adjacent angles are equal.
14. Two lines are called perpendicular if they form two right angles.
15. Two lines perpendicular to the third do not intersect.
16. Equal angles have equal degree measures.
17. The expanded angle is 180 0 .
18. If two adjacent angles are equal, then they are acute.
19. If two lines are perpendicular to the third, then they are parallel.
20. Two adjacent angles can both be obtuse.
Triangles.
1. The triangle is a three-dimensional figure.
2. A triangle is a geometric figure consisting of three points connected in pairs by segments.
3. A triangle is a geometric figure consisting of three points that do not lie on one straight line and are connected in pairs by segments.
4. If two triangles are equal, then their corresponding elements are always equal.
5. The first sign of equality of triangles is a sign of equality in a side and two angles.
6. When crossing perpendicular lines, four acute angles are obtained.
7. The median of a triangle drawn from a given vertex is a straight line connecting this vertex with the midpoint of the opposite side.
8. The median of a triangle drawn from a given vertex is the segment connecting this vertex to the midpoint of the opposite side.
9. In any triangle, only three bisectors can be drawn.
10. The bisector of any triangle is a segment.
11. The bisectors of any triangle always intersect at one point.
12. The altitude of a triangle dropped from a given vertex is the perpendicular drawn from the vertex to the opposite side of the triangle.
13. The altitude of a triangle dropped from a given vertex is the perpendicular drawn from the vertex to the line containing the opposite side of the triangle.
14. Equal sides of an isosceles triangle are called lateral.
15. Equal sides of an isosceles triangle are called bases.
16. An isosceles triangle has two sides and one base.
17. The angles at the base of an isosceles triangle are equal.
18. In an isosceles triangle, all angles are equal.
19. If the perimeter of a triangle is 60 cm and the triangle is equilateral, then the length of each side is 20 cm.
20. The third sign of the equality of triangles is a sign of equality in two sides and an angle.
21. The third sign of the equality of triangles is the sign of equality on three sides.
22. A circle is a figure consisting of points of a plane located at a given distance from a given point.
23. Diameter is the largest chord.
24. Radius is a chord.
Triangles.
1. The triangle is a flat figure.
2. In the triangle ABC, the sides adjacent to the angle CAB are AC and BC.
3. In the triangle AMC, the side opposite the angle AMC is the side AC.
4. The perimeter of the MSC triangle with sides 7 cm, 11 cm, 8 cm is 26 cm.
5. The first sign of the equality of triangles is the sign of equality in sides and angle.
6. The first sign of equality of triangles is a sign of equality in terms of sides and the angle between them.
7. When perpendicular lines intersect, four right angles are obtained.
8. Only three medians can be drawn in any triangle.
9. In any triangle, only one median can be drawn.
10. The bisector of a triangle drawn from a given vertex is a ray emerging from this vertex, passing between the sides of the angle and dividing the angle in half.
11. The bisector of a triangle drawn from a given vertex is the segment of the bisector of the angle of the triangle that connects this vertex to a point on the opposite side.
12. In any triangle, you can draw as many heights as you like.
13. In any triangle, only three heights can be drawn.
14. An isosceles triangle is called, in which two sides are equal.
15 . An isosceles triangle is one in which three sides are equal.
16. An equilateral triangle is called, in which all sides are equal.
17. In an equilateral triangle, all angles are equal.
18. The second sign of the equality of triangles is the sign of equality in a side and two angles.
19. The second sign of the equality of triangles is a sign of equality in terms of a side and two angles adjacent to it.
20. A circle is a figure consisting of all points of the plane located at a given distance from a given point.
21. In a circle, all radii have different lengths.
22. In a circle, all chords are equal.
23. Diameter is a chord passing through the center.
24. The diameter of a circle is twice the radius of the same circle.
25. In a circle, all radii are equal.
Parallel lines
1. Mark the correct statements with a “+” sign and erroneous ones with a “-” sign.
1. Parallel lines are straight lines that do not intersect.
2. Only two parallel lines can be drawn.
3. If a certain line intersects one of the two parallel lines, then it intersects the other as well.
4. If two lines are parallel to a third, then they cannot be parallel.
5. If two lines are perpendicular to the third, then they are parallel.
6. When two straight lines intersect with a third, four non-expanded angles are formed.
3 4 7. Angles 3 and 5 , 4 and 6 are called crosswise.
8. Angles 3 and 6, 5 and 4 are called crosswise.
9. Angles 3 and 5, 4 and 6 are called one-sided.
5 6 10. Angles 3 and 7, 2 and 6 are called corresponding.
7 8 11. Angles 4 and 6 , 5 and 4 are called one-sided.
12. Through a point not lying on a given line, there passes a set of lines parallel to the given one.
13. If a line intersects one of two parallel lines, then it is perpendicular to the other line.
14. If at the intersection of two lines of a secant, the lying angles are equal, then the lines are parallel.
15. If at the intersection of two lines of a secant, the sum of the cross lying angles is equal to 180 0, then the lines are parallel.
16. If two parallel lines are crossed by a secant, then the crosswise lying angles are equal.
17. If two parallel lines are crossed by a secant, then the sum of one-sided angles is 180 0 .
2. Mark the correct statements with a “+” sign and erroneous ones with a “-” sign.
1. Parallel lines are straight lines lying on a plane and not intersecting.
2. Only three parallel lines can be drawn.
3. Through any point not lying on a given line, one can draw a straight line parallel to it in the plane, and only one.
4. If two lines are parallel to the third, then they are parallel to each other.
5. When two straight lines intersect with a third, eight non-expanded angles are formed.
6. At the intersection of two straight lines of the third, two pairs of cross-lying angles are formed.
7. An axiom is a mathematical statement about the properties of figures.
8. An axiom is a mathematical statement about the properties of geometric figures, accepted without proof.
9. A straight line passes through any two points, and moreover, only one.
10. Through a point not lying on a given line, there passes only one line parallel to the given one.
11. Through a point not lying on a given line, there are only two lines parallel to the given line.
12. If two lines are parallel to the third, then they are perpendicular to each other.
13. If two lines are parallel to a third, then they are parallel to each other.
14. If at the intersection of two lines of a secant, the corresponding angles are equal, then the lines are parallel.
15. If, at the intersection of two lines, the secant sum of the corresponding angles is 180 0, then the lines are parallel.
16. If, at the intersection of two lines, the secant sum of one-sided angles is 180 0, then the lines are parallel.
17. If a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other.
18. If two parallel lines are crossed by a secant, then the corresponding angles are equal.
on the topic: “Initial concepts of planimetry. Straight line and cut. Beam and angle.
Type of lesson - ONZ.
Lesson Objectives:
I Tutorials:
Systematize information about the relative position of points and lines;
Consider the properties of a straight line;
Learn to mark points and lines in the figure;
Introduce the concept of a segment;
Remind students what a ray and an angle are; introduce the concepts of internal and external regions of a non-expanded angle, introduce various designations of rays and angles;
Start learning the ability to isolate from the text of a geometric problem what is given and what needs to be found, reflect the situation given in the condition of the problem and that arises in the course of its solution, in the figure, briefly and clearly write down the solution to the problem.
II Developing:
Development cognitive interest students;
Development of students' memory;
Development of students' curiosity.
III Educational:
Mental education (formation of logical, abstract, systemic thinking; possession of intellectual skills and mental operations - analysis and synthesis, comparison, generalization);
The formation of such personality traits as organization, discipline, accuracy.
IV Meta-subject: development of cognitive interest in the subject, the ability to find analogies and connections with other sciences.
During the classes
I. Organizing time.
Teacher: “The bell rang, the students are ready for the lesson. Let's start our lesson."
II. Reporting the topic of the lesson with a note in a notebook. Setting lesson goals for students.
III. Introductory talk about the origin and development of geometry.
Conversation plan:
1. The origin of geometry.
2. From practical geometry to the science of geometry.
3. Geometry of Euclid.
4. History of the development of geometry.
5. Geometric shapes.
Slides #2-5.
Geometry is the result practical activities people: it was necessary to build dwellings, temples, lay roads, irrigation canals, establish borders land plots and determine their size. Translated from Greek, the word "geometry" means "surveying" ("geo" - in Greek - earth, and "metreo" - to measure). This name is explained by the fact that the origin of geometry was associated with various measuring works.
The aesthetic needs of people also played an important role: the desire to decorate their homes and clothes, to paint pictures of the surrounding life. All this contributed to the formation and accumulation of geometric information.
For several centuries BC, in Babylon, China, Egypt and Greece, there already existed initial geometric knowledge, which was obtained mainly by experience, but it was not yet systematized and passed down from generation to generation in the form of rules and recipes, for example, rules for finding areas figures, volumes of bodies, construction of right angles, etc.
There was no proof of these rules, and their exposition did not constitute scientific theory. The first who began to obtain geometric facts using reasoning (proofs) was the ancient Greek mathematician Thales(6th century BC), who in his studies used the bending of the drawing, the rotation of part of the figure, and so on, that is, what is called movement in modern geometric language.
Gradually, geometry becomes a science in which most of the facts are established through conclusions, reasoning, and evidence.
Attempts by Greek scientists to bring geometric facts into a system began as early as the 5th century BC. BC e. The greatest influence on all subsequent development of geometry was exerted by the works of the Greek scientist Euclid, who lived in Alexandria in the 3rd century BC. BC e. For almost 2,000 years, Euclid's Elements served as the main book on which geometry was studied. In the "Principles" the geometric information known by that time was systematized, and geometry for the first time appeared as a mathematical science.
This book was translated into the languages of many peoples of the world, and the geometry itself outlined in it became known as Euclidean geometry.
The school geometry course is divided into planimetry And stereometry. The branch of geometry that studies the properties of figures on a plane is called planimetry (from the Latin word "planum" - plane and the Greek "metreo" - I measure). In stereometry, the properties of figures in space, such as a parallelepiped, a ball, a cylinder, a pyramid, are studied. We will begin our study of geometry with planimetry.
In geometry, shapes, sizes, and the mutual arrangement of objects are studied, regardless of their other properties: mass, color, etc. Abstracting from these properties and taking into account only the shape and size of objects, we come to the concept of a geometric figure.
Geometry not only gives an idea of the figures, their properties, mutual arrangement, but also teaches you to reason, ask questions, analyze, draw conclusions, that is, think logically.
In mathematics lessons, you got acquainted with some geometric shapes and imagine what point, line, segment, ray, angle, how they can be positioned relative to each other.
IV. Presentation of new material.
Slide number 7.
Construct two pairs of points draw lines through the points along the ruler. How many lines can be drawn through two different points?
The first characteristic property of the line is established.
Slide number 8.
The student concludes that there is only one line passing through two distinct points.
The teacher introduces students to the sign of belonging and 
. The main purpose of the slide is to encourage children to identify the second property of the line: you can build any point on it, the line has "as many" points as you like. Students naturally perceive the replacement of the phrase "any number of points" with the phrase "infinitely many points".
Slide number 9.
Working with this slide, students realize that the straight line model has not yet been obtained: the construction should be continued by moving the ruler to the right or left. The question arises: how far can one "go" with such a construction? The visibility of the operation prompts the answer: arbitrarily far, infinitely far both to the right and to the left. Hence, the line is infinite, this is its second property. That is why, as the textbook says, “from any point on a straight line, segments of any length can be put off in both directions.” The teacher reads a phrase from a textbook: "A straight line, unlike a segment, has neither beginning nor end." But the circle has neither beginning nor end. Maybe a straight line "looks" like a circle? Now we should deal with the second question of the slide: will the crocodile and the bee meet, building a straight line, one to the left, the other to the right. Usually children answer: “They won’t meet, the straight line is not like a circle, it is not closed” (another answer is also logical, but students may not be aware of it).
If in such a clear way to clarify the property of the non-closure of a straight line, then students will be able to later realize how the ray “obtains”, to see the origin of the concept.
Slide number 10.
This slide is shown as a summary. The ability to refer to this or that property will indicate that the concept of a straight line has been formed in the student's thinking.
Performing a physical education session by students to improve cerebral circulation:
And physical exercises for the eyes:
Slide number 11.
It is natural to put the question before the students: is it possible to explain how a segment is obtained? Let's use a slide. At the same time, the term "between" is perceived by intuition.
Slides 12 and 13.
Students solve problem No. 5 and problem No. 7 (the text of the tasks is given on the slides). These problems can be solved together with the teacher's comments (or you can show the answer for the student to check their solution).
Slide number 14.
The teacher introduces the concept of a beam. The line AB and the point O belonging to it are constructed. Drawing received. The teacher suggests painting the point O and the part of the straight line to the right of the point O, for example, in pink. It turned out a new figure - a ray. Its receipt is described on the slide "beam". Rays are constructed, a designation is introduced, children find out why the ray is infinite away from the beginning. A ray is obtained as the union of a point on a line and one of the parts into which this point divides the line.
Slide number 15.
To consolidate the concept, children perform task No. 8 of the textbook (the text of the task is given on the slide).
Slide number 16.
The formation of the concept of an angle is carried out approximately in the same way as the concepts of intersection and union of figures (for example, as a ray was introduced earlier). Students build two different beams with a common beginning. Remembering that the beam is infinite, the children find out that the constructed two beams with a common origin divide the plane into two regions. One of the areas is proposed to be painted over. The fact that the rays and the selected area are colored in the same color means that their union has been built. The resulting figure is called an angle. How is an angle built? The teacher encourages students to write a description of the concept using this slide. Enter the designation of the corners.
slide number 17.
Slides 18 and 19.
Students perform exercises that contribute to the formation of the concept of an angle and the formation of the concept of intersection of figures. These exercises are especially interesting, they will allow you to find out whether the concept is formed.
Students performing physical exercises for the eyes:Close your eyes tightly (count to 3, open them and look into the distance (count to 5). Repeat 4-5 times.
V. Consolidation of the studied material.
slide number 20.
The teacher asks students to complete the following tasks on their own:
In Figure 1, answer the questions:
1. Write down all segments.
2. Write down all lines.
3. Which points belong to the line AD and which do not? Write your answer using math symbols.
4. Pick a point that belongs to both line BC and line AC. What is another name for this point?
5. According to figure 2, write down the points belonging to:
A) the outer region of the corner;
B) the inner region of the corner;
Self Test Answers:
1. AB, BD, AD, DC, BC, DM, AM.
Students sum up the lesson, answer orally the questions of the teacher:
1) What did they learn?
2) what is "geometry"?
3) what sections of geometry exist?
4) what basic concepts were discussed in the lesson?
5) what is "straight line"? "line segment"? "Ray"? "corner"?
VII. Grading the lesson with the teacher's commentary.
VIII. Homework(slide number 22):
Literature:
1) L. S. Atanasyan, V. F. Butuzov and others. Geometry: textbook. for 7-9 cells. general education institutions. - M .: Education, 2010 .
2) Gavrilova N. F. Pourochnye development in geometry. 7th grade. M.: "VAKO", 2010.
Lesson topic: Initial geometric information. Straight line and cut.
Target: to acquaint students with a new subject for them, with the history of the development of geometry, with the main geometric figures on the plane;
Tasks :
form the concept of a geometric figure, as a set of points;
systematize students' knowledge about the relative position of points and lines;
to form an understanding of the relationship between mathematics and objective reality.
Orgmoment
Message about the topic and purpose of the lesson
Learning new material
1. Introductory conversation
Today we begin the study of a new mathematical subject of geometry, which is an integral part of big science mathematics.
You are already familiar with many geometric shapes. List them and point them out in the classroom.
Geometry (Greek) - “geos” - earth, “metreo” - I measure.
Geometry is the science of the properties of geometric shapes.
Geometry has a wide application in the work of people of different professions.
Also in Ancient Greece on the gates of the academy were carved the words: "Let no one who does not know geometry enter here."
The ancient Greek historian Herodotus (5th century BC) about the origin of geometry in ancient Egypt around 2000 BC. wrote as follows: “The Egyptian pharaoh divided the land, giving each Egyptian a plot of land by lot, and levied a tax on each plot. It happened that the Nile flooded a particular area, then the victim turned to the King, and the king sent surveyors to establish how much the area had decreased, and accordingly reduce the tax. So geometry arose in Egypt, and from there it passed to Greece.
Geometry as a science arose as a result of human practical activity (tanner, builder, etc.). A person came across geometric shapes and their properties in Everyday life to the study of geometric figures and their properties, i.e. to the study of geometry.
For several centuries BC. in Babylon, China, Egypt and Greece, elementary geometric knowledge already existed, but they had not yet been systematized and were usually reported in the form of rules and recipes - to determine, for example, the areas of figures, volumes of bodies, etc. They had no evidence and the presentation was not was a scientific theory.
There is a need to systematize knowledge. The first attempt was made by Hippocrates (there were other attempts) But all these attempts were forgotten when Euclid's immortal work "Beginnings" appeared in the III B.E.
No scientific book has enjoyed such centuries-old success as Euclid's Elements. It has been the main textbook for almost 2000 years.
The geometry that we study at school is called Euclidean.
7-9 cells - study the section of geometry - pnimetry. It studies the properties of figures on a plane (line segments, triangle, rectangles, circle, circle, etc.)
Can we study the cube in planimetry?
Let's start the study of planimetry with the study of the basic geometric shapes, which are - a point, a straight line. Consider how a point and a line are drawn.
2.Main material
What is a geometric figure made up of? (from dots)
To depict a straight line in a drawing, use a ruler (only part of the straight line is shown)
a) The line is infinite
Draw a straight line. Does a straight line have ends?
b) Designation
straight line - a,b, c, d, e, fetc.
dot -A, B, C, D, E, Fetc.
c) Mark 2 points on the line and 1 outside it.
A a, B a, C A
d) How many points can be marked on the line and outside it? (∞)
e) Mark 1 point and draw straight lines through it.
Through 3 points.
Through 2 points
How many lines can be drawn?
Through any 2 points you can draw a line, and moreover, only one .
e)a b - A, e d- no common points
g) cannot have 2, etc. common points, becauseaxiom
g) - part of a straight line bounded by two points
[ AB] A, B - the ends of the segment
Application of knowledge in a standard situation
№ 1, № 2, № 4, №7
Summarizing
How many lines can be drawn through one point, through two points?
Can the lines OA and AB be different if the point OAB ( no, because both of them pass through A and O, and only one line passes through two points)
Given 2 straight linesA And b , intersecting at point C, and the pointDb(no, because 2 lines cannot have 2 common points )
Geometry is one of the most ancient sciences. The first geometrical facts are found in the Babylonian cuneiform tables and Egyptian papyri. (III millennium BC), as well as in other sources. The name of the science "geometry" of ancient Greek origin, it is composed of two ancient Greek words: "ge" - "earth" and "metreo" - "I measure" (I measure the earth).
Geometry - is a branch of mathematics that studies geometric shapes and their properties.
1 . Draw a straight line. How can it be labeled?
2 . Mark point C, not lying on the given line, and points D , E , K , lying on the same line .
Ownership symbols
belongs does not belong
3 . Using membership symbols, write the sentence "Point D belongs to the line AB , and point C does not belong to the line A ".
4 . Using the drawing and membership symbols, write down which points belong to the line b , and which are not.
How many lines can be drawn through a given point A?
— How many lines can be drawn through two points?
Can a line be drawn through any two points?
5 .Draw straight lines XY And MK , intersecting at a point ABOUT .
To jot down that direct XYAndMK intersect at a point ABOUT, use the symbol ∩ and write it like this: XY ∩ MK = O.
How many common points can two lines have?
6. On a straight line A mark consecutive points A , B , C ,D . Write down all the resulting segments.
7 . draw straight lines A And b , intersecting at a point M. On straight A mark a point N , different from the point M .
a) Are the lines MN And A different lines?
b) Can a straight line b pass through a point N ?
Solve problems:
1) How many points of intersection can three lines have? Consider all possible cases and make appropriate drawings.
| Explanatory note |
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| Belichenko Anna Vladimirovna, teacher of mathematics |
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| Resource name | Initial geometric information. Straight line and cut. |
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| Resource type | Presentation + lesson summary |
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| Subject, UMK | Geometry, UMK L. S. Atanasyan |
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| The purpose and objectives of the resource | Introduce the concept of "geometry", form an idea of \u200b\u200bgeometry as a science. Enter the terms "Point. Straight. Segment. ”, to be able to distinguish between these concepts in the process of studying new material. |
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| Age of students for whom the resource is intended | ||
| The program in which the resource was created | Microsoft Power, Word |
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| Computer, projector + screen |
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| Sources of information (required!) |
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| Fon-Baeva Natalya Vladimirovna, teacher primary school MKOU "Novoyarkovskaya secondary school" Kamensky district Altai Territory, "Books"; https://en.wikipedia.org/wiki/%D0%A1%D0%B2%D0%BE%D0%B9%D1%81%D1%82%D0%B2%D0%BE https://yandex.ru/images http://easyen.ru/ |
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"The first lesson in the 7th grade on the geometry of UMK Atanasyan L"
The first lesson in the 7th grade on the geometry of UMK Atanasyan L. S.« Initial geometric information. Straight line and cut»
Belichenko Anna Vladimirovna,
mathematic teacher
Lesson Objectives: Introduce the concept of "geometry", form an idea of \u200b\u200bgeometry as a science. Enter the terms "Point. Straight. Segment”, to be able to distinguish between these concepts in the process of studying new material.
During the classes
Organizing time. Safety briefing in the mathematics classroom. Rules of conduct and work in the mathematics classroom, in geometry lessons.
Introduction to the topic of the lesson.
(Slide 11) Straight property.
Through any two points you can draw a straight line and only one.
(Slide 12)
Consolidation of what has been learned.
(Slide 13) We consider the correct design of tasks. From textbook number 2, 3, 5.
Independent work . Independent work is carried out in the form of a dictation on sheets and submitted to the teacher for verification.
Answers:
b M E
M b , E b
3. 3 intersection points, 1 intersection point, 2 intersection points, no intersection points.
Homework. p. 1.2, answer questions 1-3 on p. 25, no. 1, 4, 6, 7
View presentation content
"First geometry lesson in 7th grade"
The first lesson in the 7th grade in geometry UMK Atanasyan L. S. “Initial geometric information. Straight line and segment "
Belichenko Anna Vladimirovna
mathematic teacher
MBOU secondary school №17
Kavkazsky district, Kropotkin
Thales
Euclid
Lobachevsky N.I.
Maurice Cornelius Escher "Ascent and Descend"
Maurice Cornelius Escher "Waterfall"
You already know some geometric shapes
corner
triangle
rectangle
circle
. dot
straight
line segment
stereometry
planimetry
A segment is a part of a straight line bounded by two points. points A And B- segment ends
A segment with ends A and B is designated AB or BA.
It contains points A and B and all points of the line between points A and B.
A line can be defined in two ways:
- small latin letter,
- two capital Latin letters.
How many lines can be drawn through a given point?
How many lines can be drawn through two points?
Can a line be drawn through any two points?
Straight property. Through any two points you can draw a straight line and only one.
XY ∩ MK = O
Two lines can have either one common point or no common point.
№ 1
Find: FE - ?
FE = 8 - 5 = 3 cm
Answer: 3 cm
Independent work
1. Draw a line and label it with a letter b. mark a point M lying on this line and mark a point E not lying on this line. Using the symbolism belongs - є, does not belong - є, write down the sentence "Point M lies on the line b, and point E does not lie on it."
2. Three points are given on the plane. How many lines can be drawn through these points so that at least two of the given points lie on each line? Make a drawing.
3. How many points of intersection can three lines have?
- § 1, 2, questions 1 - 3, p.25
- № 1, 4, 6, 7
- L. S. Atanasyan, "Geometry, grades 7-9", Moscow, Education;
- Background - Baeva Natalya Vladimirovna, primary school teacher, MKOU "Novoyarkovskaya secondary school" Kamensky district Altai Territory, "Books";
- T. M. Mishchenko, “Geometry. Thematic tests, grade 7, Moscow, Education;
- G. Yu. Kovtun, “Geometry. Technological cards, 7th grade";
- N. F. Gavrilova, “Universal lesson developments in geometry, grade 7 ";
- https://en.wikipedia.org/wiki/%D0%A1%D0%B2%D0%BE%D0%B9%D1%81%D1%82%D0%B2%D0%BE
- https://yandex.ru/images
- http://easyen.ru/
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