on the topic: “Initial concepts of planimetry. Straight line and segment. Beam and Angle".
Lesson type - ONZ.
Lesson objectives:
I Educational:
Systematize information about the relative positions of points and lines;
Consider the properties of a straight line;
Learn to designate points and lines in a drawing;
Introduce the concept of a segment;
Remind students what a ray and an angle are; introduce the concepts of internal and external areas of an undeveloped angle, introduce various notations for 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 conditions of the problem and arising in the course of solving it in a drawing, briefly and clearly write down the solution to the problem.
II Developmental:
Development of students' cognitive interest;
Development of students' memory;
Developing students' curiosity.
III Educational:
Mental education (formation of logical, abstract, systematic thinking; mastery of intellectual skills and mental operations - analysis and synthesis, comparison, generalization);
Formation of such personality qualities 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. Report the topic of the lesson with a note in a notebook. Setting lesson goals for students.
III. Introductory conversation about the emergence 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 No. 2-5.
Geometry arose as a result of the practical activities of people: it was necessary to build houses, temples, lay roads, irrigation canals, establish the boundaries of land plots and determine their sizes. Translated from Greek, the word “geometry” means “land surveying” (“geo” means earth in Greek, and “metreo” means 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 life around them. All this contributed to the formation and accumulation of geometric information.
Several centuries BC in Babylon, China, Egypt and Greece, basic geometric knowledge already existed, which was obtained mainly experimentally, but it was not yet systematized and was passed on 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 yet, and their presentation did not constitute a 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 research used bending the drawing, rotating part of the figure, and so on, that is, what in modern geometric language is called movement.
Gradually, geometry becomes a science in which most facts are established through conclusions, reasoning, and evidence.
Attempts by Greek scientists to bring geometric facts into a system began already in the 5th century. 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 e. Euclid's work “Elements” served as the main book for studying geometry for almost 2000 years. In the “Principles” the geometric information known by that time was systematized, and geometry first appeared as a mathematical science.
This book was translated into the languages of many peoples of the world, and the geometry presented in it began to be called 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 sphere, a cylinder, and a pyramid, are studied. We will begin our study of geometry with planimetry.
In geometry, the shapes, sizes, and relative positions 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 shapes, their properties, and relative positions, but also teaches one to reason, pose questions, analyze, draw conclusions, that is, to think logically.
In mathematics lessons you became acquainted with some geometric figures and can imagine what point, straight line, segment, ray, angle, how they can be located relative to each other.
IV. Presentation of new material.
Slide number 7.
Construct two pairs of points and draw lines through the points using a 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 straight line passing through two different 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 a straight line: you can construct any point on it, a straight line has “as many” points as you like. Students naturally accept replacing the phrase “as many points as you like” with the phrase “infinitely many points.”
Slide number 9.
Working with this slide, students realize that the model of the straight line 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 you “go” with such a construction? The clarity of the operation prompts the answer: as far as you like, infinitely far, both to the right and to the left. This means that the line is infinite, this is its second property. That is why, as the textbook says, “from any point on a straight line you can lay off segments of any length in both directions.” The teacher reads a phrase from the textbook: “A straight line, unlike a segment, has neither beginning nor end.” But a circle has neither beginning nor end. Maybe a straight line “looks” like a circle? Now we should tackle the second question of the slide: will a crocodile and a bee meet, constructing a straight line, one to the left, the other to the right. Usually children answer: “They won’t meet, a 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 this visual way we find out the property of non-closedness of a straight line, then students will be able to then understand how a ray is “produced” and see the origin of the concept.
Slide number 10.
This slide is shown to summarize. 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.
Students performing physical education to improve cerebral circulation:
And physical exercises for the eyes:
Slide number 11.
It is natural to ask students: is it possible to explain how a segment is obtained? We use a slide. In this case, the term “between” is perceived by intuition.
Slides No. 12 and 13.
Students solve problem No. 5 and problem No. 7 (the text of the problems is given on the slides). These problems can be solved along with the teacher's comments (or the answer can be shown so that the student checks his solution).
Slide number 14.
The teacher introduces the concept of a ray. A straight line AB and a point O belonging to it are constructed. Drawing received. The teacher suggests painting point O and part of the line lying to the right of point O, for example, pink. The result is a new figure - a ray. Its production is described on the “beam” slide. The rays are constructed, the notation is introduced, and the children find out why the ray is infinite away from the beginning. The 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 complete 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 in approximately the same way as the concepts of intersection and union of figures (for example, as the ray was previously introduced). Students build two different beams with a common beginning. Remembering that the ray is infinite, children find out that the constructed two rays 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 the same color means that their union has been constructed. The resulting figure is called an angle. How is the angle constructed? The teacher encourages students to create a description of the concept using this slide. Enter the designation of angles.
Slide number 17.
Slides No. 18 and 19.
Students perform exercises that promote 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 has been formed.
Students performing physical education 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 material being studied.
Slide number 20.
The teacher asks students to complete the following tasks independently:
Based on Figure 1, answer the questions:
1. Write down all the segments.
2. Write down all the lines.
3. Which points belong to the line AD and which do not? Write your answer using mathematical symbols.
4. Indicate a point that belongs to both the straight line BC and the straight line AC. What else can you call the indicated point?
5. According to Figure 2, write down the points belonging to:
A) the outer area of the corner;
B) the inner area of the corner;
Self-test answers:
1. AB, BD, AD, DC, BC, DM, AM.
Students summarize the lesson and answer the teacher’s questions orally:
1) what new did they learn?
2) what is “geometry”?
3) what branches of geometry exist?
4) what basic concepts were covered in the lesson?
5) what is “straight”? "line segment"? "Ray"? "corner"?
VII. Giving a grade for a lesson with a comment from the teacher.
VIII. Homework (slide number 22):
Literature:
1) Atanasyan L. S., Butuzov V. F. and others. Geometry: textbook. for 7-9 grades. general education institutions. - M.: Education, 2010.
2) Gavrilova N. F. Lesson developments in geometry. 7th grade. M.: "VAKO", 2010.
Lesson topic: Basic geometric information. Straight line and segment.
Target: introduce students to a new subject for them, to the history of the development of geometry, to the basic geometric figures on a plane;
Tasks :
form the concept of a geometric figure as a set of points;
systematize students’ knowledge about the relative positions of points and lines;
to form an understanding of the relationship between mathematics and objective reality.
Organizational moment
Communicating the topic and purpose of the lesson
Learning new material
1.Introductory conversation
Today we are starting to study the new mathematical subject of geometry, which is an integral part of the larger science of mathematics.
You are already familiar with many geometric shapes. List them and display them in the classroom.
Geometry (Greek) – “geos” - earth, “metreo” - measure.
Geometry is the science of the properties of geometric figures.
Geometry has wide application in the work of people of different professions.
Even in Ancient Greece, the words were carved on the gates of the academy: “Let no one who does not know geometry enter here.”
Ancient Greek historian Herodotus (5th century BC) about the origin of geometry in Ancient Egypt around 2000 BC. wrote this: “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 this or that plot, then the victim turned to the Tsar, and the Tsar sent surveyors to determine how much the plot had decreased and reduce the tax accordingly. This is how geometry arose in Egypt, and from there it moved to Greece.”
Geometry as a science arose as a result of the practical activities of man (leatherworker, builder, etc.). A person came across geometric figures and their properties in everyday life to the study of geometric figures and their properties, i.e. to the study of geometry.
Several centuries BC. in Babylon, China, Egypt and Greece, basic geometric knowledge already existed, but it had not yet been systematized and was usually communicated in the form of rules and recipes - to determine, for example, the areas of figures, volumes of bodies, etc. There was no evidence in them 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 “Elements” appeared in the 3rd century AD.
No scientific book has enjoyed such centuries-old success as Euclid's Elements. It was the main textbook for almost 2000 years.
The geometry we study at school is called Euclidean.
7-9 grades - study the section of geometry - plnimetry. It studies the properties of figures on a plane (segments, triangle, rectangles, circle, circle, etc.)
Can we study the cube in planimetry?
We begin our study of planimetry by studying the basic geometric figures, which are a point and a straight line. Let's look at how a point and a line are depicted.
2.Main material
What is any geometric figure made of? (from dots)
To depict a straight line in a drawing, use a ruler (only part of the straight line is depicted)
a) The straight 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.
After 3 points.
Through 2 points
How many straight lines can you draw?
Through any 2 points you can draw a straight line, and only one .
e)a b - A, e d– no common points
e) cannot have 2, etc. common points, becauseaxiom
g) – part of a line bounded by two points
[ AB] A, B – 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 and through two points?
Can straight lines OA and AB be different if point OAB ( no, because they both pass through A and O, and only one straight line passes through two points)
Given 2 straight linesA And b , intersecting at point C, and pointDb(no, because 2 lines cannot have 2 points in common )
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Slide captions:
Galileo Galilei “Nature speaks the language of mathematics: the letters of this language are circles, triangles and other mathematical figures”
Geometry is one of the most ancient sciences, originating more than 4000 years ago. The word geometry is of Greek origin. Literally it means "land surveying". "geo" - earth in Greek, "metreo" - to measure
This science, like others, arose from human needs: it was necessary to build temples, dwellings, lay roads and irrigation canals, determine the boundaries of land plots and their sizes. The aesthetic needs of people also played an important role: to paint pictures, decorate clothes and homes. All this contributed to the acquisition and accumulation of geometric information. At the time of the birth of geometry, the rules were derived on the basis of information and facts obtained experimentally, so science was not accurate. Gradually, geometry became a science in which most facts are established through inference, reasoning, and evidence.
The first who began to obtain new geometric facts using reasoning (evidence) was the ancient Greek scientist Thales (VI century BC). Thales (ancient Greek Θαλῆς ὁ Μιλήσιος, 640/624 - 548/545 BC) - ancient Greek philosopher and mathematician from Miletus (Asia Minor). Representative of Ionic natural philosophy and founder of the Milesian (Ionian) school, with which the history of European science begins. Traditionally considered the founder of Greek philosophy (and science)
The greatest influence on the subsequent development of geometry was exerted by the works of the Greek scientist Euclid. In the 3rd century. BC. he wrote the essay “Principia”, and for almost 2000 years geometry was studied from this book, and the science was named Euclidean geometry in honor of the scientist. Euclid is the first mathematician of the Alexandrian school. His main work, “Principia,” contains an exposition of planimetry, stereometry, and a number of questions in number theory; in it he summed up the previous development of ancient Greek mathematics and created the foundation for the further development of mathematics.
Geometry planimetry stereometry Part of geometry that deals with figures on a plane (straight line, line segment, ray, angle, polygon) Part of geometry that deals with figures in space (ball, cube, cylinder, pyramid) Geometry is the science that deals with the study of geometric figures
Draw a straight line. How can it be designated? 2. Mark point C, which does not lie on this line, and points D, E, K, lying on the same line. 3. Using symbols of belonging, write down the sentence: “Point K belongs to line AB, point C does not belong to line a.”
Draw two intersecting lines. Mark the lines and the point of intersection. How many common points can two lines have in common? Two lines either have one common point or have no common points.
2. Mark two points A and B. Draw a line passing through these points. 1. Mark point A. Draw three lines a, b and c passing through this point. How many lines can be drawn through a given point A? Draw another line passing through these points. How many lines can be drawn through two points? Can you draw a straight line through any two points? Through any two points you can draw a straight line, and only one. Through a given point A you can draw many straight lines.
The part of the line bounded by two points is called Segment A and B - the ends of the segment AB
1. Draw a straight line, mark it with the letter a. Mark points A, B, C, D lying on this line. Write down all the resulting segments 2. Draw lines m and n intersecting at point K. On line m, mark point M, different from point K. a) Are lines KM and m different lines? b) Are the lines KM and n different lines? c) Can straight line n pass through point M?
1. What is the meaning of the technique “Hanging a straight line”? 2. Where is this technique used in practice? 3. Is it possible to use this technique in educational activities?
1st level of difficulty: 1. No. 2, 5, 6 (textbook) 2nd level of difficulty: 1. How many points of intersection can three straight lines have? Consider all possible cases and make appropriate drawings. 2. Three points are given on a plane. How many lines can be drawn through these points so that at least two of these points lie on each line? ? Consider all possible cases and make appropriate drawings.
1. What is the name of the science that deals with the study of geometric figures 2. What is the name of the part of geometry in which figures on a plane are considered 3. What is the name of the part of geometry in which figures in space are considered 4. How many lines can be drawn through two points? 5. How many points of intersection can two straight lines have?
Textbook: paragraphs 1, 2; questions 1-3 (p. 25) Textbook: No. 1, 3, 4, 7. Additional task: How many different lines can be drawn through four points? Consider all cases and make corresponding drawings.
On the topic: methodological developments, presentations and notes
Introductory geometry lesson in 7th grade "A brief history of the origin and development of geometry. Basic geometric information"
Introductory geometry lesson in the 7th grade using multimedia "A brief history of the origin and development of geometry. Basic geometric information" Type: combined, with...
Municipal budgetary educational institution "Nizhneshitsinskaya secondary school Sabinsky district of the Republic of Tatarstan"
Methodological development of an open geometry lesson in 7th grade Topic: Basic geometric information. Dots. Direct. Segments
Mathematics teacher Gulyusa Airatovna Gafiyatova
Saba 2013
Lesson type:lesson - introduction to a new subject.
Methods and techniques for teaching a lesson:
1.Working with the textbook
2. Frontal work with the class
3.Individual work with students.
Lesson objectives:
1.
Educational:
acquaintance with the structure, basic concepts and history of the development of geometry.
2.
Educational:development of spatial imagination, creative thinking, cognitive interest of students, interdisciplinary connections, culture of mathematical speech.
3.
Educational:nurturing respect among students for each other in the process of educational activities, self-control and self-esteem, respect for educational work
Equipment:interactive whiteboard, computer, models of geometric shapes, landscape sheets, colored markers, reference notes. Lesson structure
DURING THE CLASSES
I.Organizing time
Teacher:- Hello guys! Sit down! Today we are starting to study a new subject - geometry. You probably have questions: -What is “geometry”? What is she studying? Teacher: Geometry is an integral part of a big science - mathematics. It would be wrong to say that until now you have not studied geometry at all and know nothing about it. You have often encountered triangles and pyramids, squares and cubes, circles and balls. Maybe not much, but you know something about these bodies and figures, you have a good idea of what they look like, and you understand that they all have to do with geometry. The statement that we are beginning to study geometry means, first of all, that we are beginning a systematic course in geometry. This, in turn, means that we will gradually, step by step, build a geometric theory, consistently proving our statements, deriving them from those already known in accordance with mathematical laws. First of all, what is geometry? Have you ever heard the word “geometry”? You have been studying the subject “geography” since the sixth grade. And you probably know what the word “geo” means. What about “metrics”? (Students' answers) The word “geometry” is Greek, it is composed of two parts “geo” and “metry” and is literally translated into Russian as “land-measurement”.
Teacher:Let's continue our fairy tale. And Dunno has more questions:
- Why did the same teacher come who taught mathematics last year? A very smart teacher probably knows several subjects? And whoever came up with this - geometry, now suffer, learn another subject.
Teacher: - Yes, because geometry is only one of many branches of mathematics. The word "mathematics" comes from the ancient Greek μάθημα (máthēma), which means studying, knowledge, the science.
Mathematics how academic discipline is divided into several sections: 1.
Arithmetic (this section is studied in primary and 5-6 grades.) 2.
Elementary algebra and elementary geometry. Therefore, at school mathematics, algebra and geometry are taught by one teacher, a mathematics teacher. II.Familiarization with historical material
-And, if we look at the history of geometry, we will see a lot of interesting things. (Student's speech) How did geometry come about? As Eudemus of Rhodes said: “Geometry was discovered by the Egyptians and arose in the measurement of the earth. This dimension was him
necessary due to the flooding of the Nile, which constantly washed away the borders. It is not unusual that this science, like others, arose from human needs.” This means that geometry arose from the practical activities of people.
It was necessary to build dwellings, temples, build roads, irrigation canals, establish the boundaries of land plots and determine their sizes.
Satisfying their aesthetic needs, people decorated their homes and clothes with ornaments. Mastering the world around them, people became familiar with geometric shapes, they began to learn to measure areas, lengths, and volumes.
Occupations of people in ancient times:
ü
Construction of temples and houses;
ü
Decorating dishes and dwellings with ornaments;
ü
Marking the ground, measuring distances and areas, volumes of vessels.
Several centuries BC, in Babylon, China, Egypt, and Greece, initial geometric knowledge already existed, which was obtained experimentally and then systematized. The first who began to obtain new geometric facts using reasoning was the ancient Greek mathematician Thales (6th century BC). Gradually geometry becomes a science. WITH V century BC, the attempt of Greek scientists to bring geometric facts into a system begins. The work of the Greek scientist Euclid, Elements, was the main book used to study geometry for almost 2000 years. The geometry set forth in it came to be called Euclidean geometry.
Euclid is a famous ancient Greek mathematician, born in Athens around
Founders of geometry:
Plato founded a school whose motto is “Those who do not know geometry are not admitted!” (2400 years ago), Thales of Miletus (640-
Teacher:If you want to learn more about the history of geometry and get to know the founders of geometry better, you can click on the names of famous mathematicians and find out detailed information.
Watch a video about the importance of geometry.
III.Learning new material. Dive into the problem
-Pay attention to the board. There are geometric shapes there. And we need to divide them into two groups. What two groups will we divide them into?
Yes, right. By what principle are these geometric figures written in two different groups? (1 on the plane, 2 in space). The part of geometry that deals with figures on a plane is called planimetry, and the other part of geometry that deals with figures in space is called stereometry. We will begin our study of geometry with planimetry. Teacher:
The topic of today's lesson: “Dots. Direct. Segments." Write the topic of the lesson in your notebook. The tools needed for construction are a pencil and a ruler.-In geometry lessons we will need: Pencil, ruler, compass, protractor. And therefore, every student should have these tools in geometry lessons. Now you and I will complete tasks.The largest building is made up of small bricks, and complex geometric shapes are made up of the simplest shapes. One of them - dot.
The point is the result of an instant touch, an injection.Teacher:
Points are designated in capital Latin letters. In our case, we marked points A. 2.Draw a straight line. How can it be designated? (Direct a or MR) 1.
Mark point C, which does not lie on the given line, and points D, E. K , lying on the same line.. WITH
Teacher:
In mathematics, there are special symbols that allow you to briefly write down a statement. The symbols € and € are called membership symbols. They mean “belongs” and “does not belong” respectively.1.
Using membership symbols, write down the sentence “Point P belongs to line AB, but points K and C do not belong to line a.”2.
(P €AB, K, C € a)
3.
Using the drawing and membership symbols, write down which points belong to the line c and which do not?- How many lines can be drawn through a given point A? (Through a given point A, many straight lines can be drawn.)- How many lines can be drawn through two points? (one straight line)- Can you draw a straight line through any two points? (Yes)- What conclusion can we draw?So, through any two points you can draw a straight line and, moreover, only one.
6.Draw lines AB and MT intersecting at point O.In order to briefly write down that lines AB and MT intersect at point O, use the symbol ∩ and write it like this: AB∩MT=O
7. On straight line a, mark points A, B, X, Y in sequence. Write down all the resulting segments.
Physical education minute
Teacher:
And now it's time to rest. I will tell you geometric figures, if they are viewed on a plane, then you must sit down, and if they are viewed in space, jump on the spot.Straight line, cube, broken line, cylinder, segment, ball, ray, cone, rectangle, pyramid, square, parallelepiped. I.Solving fun problems.
Solve the puzzle
I.Checking the degree of mastery of the material
2.
Crossword solution
Test in the program
Excel
VI. Summing up the lesson
- What does geometry study?- What can we say about two lines passing through the same two points?- How many points in common can two straight lines have?Homework assignment
Teacher:
Open your diaries and write down your homework: point 1, solve No. 1, 4, do all drawings only with drawing tools.Choose a face that suits your mood after the lesson and draw it in your notebook. The lesson is over. All the best, goodbye.
Primary geometric information Grade 7 Geometric dictations Crossword puzzles This is interesting Initial geometric information Comparison of segments and angles Adjacent and vertical angles Initial geometric information Definitions of geometric figures Comparison of segments and angles Adjacent and vertical angles Initial geometric information Geometric dictation Look at the picture and write down the figures that stereometry studies Look at the picture and write down the shapes that planimetry studies Write down the geometric shapes that make up this figure Write down the geometric shapes that make up this figure How many rectangles are there in this picture? Comparison of segments and angles Dictation Task 1 Points A, B, C, D and E lie on the same straight line. Place them on a straight line so that point C lies between A and B, and point E lies between B and D. Name the segment that has the greatest length. Task 2 How many angles are shown in the figure? How many sharp angles are there in the picture? How many right angles are there in the picture? Task 3 Look at the picture. In your notebook, draw an object that has right angles. How many are there? Task 4 Look around and write down objects that have right, acute or obtuse angles. Try to draw them. Adjacent and vertical angles Dictation Task 1 Look at the picture. Name the adjacent angles. Name the vertical angles. Name the angles that add up to 180 degrees. 2 3 1 4 6 5 Task 2 Draw two straight lines so that when they intersect, two equal adjacent angles are formed. What are these straight lines called? How many right angles do you have in your drawing? Task 3 Construct two adjacent angles so that the ratio of their degree measures is also equal to 5: 4. What is the degree measure of each angle? Is there a right angle in the picture? Basic geometric information 1 2. Section of geometry that studies the properties of figures on a plane Write down geometric figures: 4 6 3 3 5 4 6 5 1 2 Definitions of geometric figures 1. A geometric figure consisting of a point and two rays emanating from this point. 2. Part of a line bounded by two points. 3.An angle whose sides lie on the same straight line. 3 4.Shapes that coincide when superimposed. 5.An angle equal to 90 degrees. 6. One of the main figures of planimetry. 4 5 6 1 Adjacent and vertical angles 1.Two intersecting lines, 1 forming four right angles. 2. If the sides of one 2 angle are a continuation of the sides of the other, then 3 angles... 3. Two angles in which one side is common, and the other two are a continuation of each other, are called... 4. A device for constructing right angles on the ground 4 Comparison of segments and angles 1.A tool for measuring angles. 2. Angle less than 90 degrees. 3. A ray emanating from 1 vertex of an angle and dividing it in half. 4. A point dividing a segment in half. 5. Distance between the ends of the segment. 2 3 6. A tool for measuring distances on the ground 4 5 6 If you want to learn about the development of geometry in the East, Greek geometry, geometry of new centuries, then go to the website articles.excelion.ru If you are interested in various types of geometry such as affine, projective or Lobachevsky's geometry, visit the site ru.wikipedia.org If you want to know about three famous problems of antiquity: On the squaring of the circle, Trisection of an angle or the Problem of doubling the cube, go to the site mediaget.ru and read If you want to know about the development of geometry in the East, Greek geometry, geometry of new centuries, then go to the site articles.excelion.ru If you are interested in different types of geometry such as affine, projective or Lobachevsky geometry, visit the site ru.wikipedia.org If you want to know about three famous problems of antiquity: On quadrature circle, Trisection of an angle or the Problem of doubling a cube, go to mediaget.ru and read