All three-dimensional geometric shapes and their names. Start in science

Figure is an arbitrary set of points on the plane. A point, a straight line, a segment, a ray, a triangle, a circle, a square, and so on are all examples of geometric shapes.

Dot– the basic concept of geometry, it is an abstract object that has no measuring characteristics: no height, no length, no radius.

Line- this is a set of points sequentially located one after another. Only the length of a line is measured. It has no width or thickness.

Straight line- this is a line that does not bend, has neither beginning nor end, it can be continued endlessly in both directions.

Ray- this is part of a straight line that has a beginning but no end; it can be continued endlessly in only one direction.

Line segment is a part of a straight line bounded by two points. A line segment has a beginning and an end, so its length can be measured.

Crooked line is a smoothly curving line, which is determined by the location of its constituent points.

broken line is a figure that consists of segments connected in series at their ends.

Vertices of a broken line- This

1. the point from which the broken line begins,
2. points at which the segments that form a broken line are connected,
3. the point at which the broken line ends.

Links of a broken line– these are the segments that make up the broken line. The number of links of a polyline is always 1 less than the number of vertices of a polyline.

Open line is a line whose ends are not connected together.

Closed line is a line whose ends are connected together.

Polygon is a closed broken line. The vertices of the polygon are called the vertices of the polygon, and the segments are called the sides of the polygon.

Lesson Objectives:

• Cognitive: create conditions for familiarization with concepts flat And volumetric geometric shapes, expand your understanding of the types of volumetric figures, teach how to determine the type of figure, and compare figures.
• Communicative: create conditions for developing the ability to work in pairs and groups; fostering a friendly attitude towards each other; to cultivate mutual assistance and mutual assistance among students.
• Regulatory: create conditions for the formation of plan learning task, build a sequence of necessary operations, adjust your activities.
• Personal: create conditions for the development of computing skills, logical thinking, interest in mathematics, the formation of cognitive interests, intellectual abilities of students, independence in acquiring new knowledge and practical skills.

Planned results:

personal:

• formation of cognitive interests and intellectual abilities of students; formation of value relations towards each other;
  independence in acquiring new knowledge and practical skills;
• formation of skills to perceive, process received information, and highlight the main content.

meta-subject:

• mastering the skills of independent acquisition of new knowledge;
• organization educational activities, planning;
• development theoretical thinking based on developing the ability to establish facts.

subject:

• master the concepts of flat and three-dimensional figures, learn to compare figures, find flat and three-dimensional figures in the surrounding reality, learn to work with development.

UUD general scientific:

• search and selection of necessary information;
• application of information retrieval methods, conscious and arbitrary construction of speech utterances orally.

UUD personal:

• evaluate your own and others’ actions;
• demonstration of trust, attentiveness, goodwill;
• ability to work in pairs;
• express a positive attitude towards the learning process.

Equipment: textbook, interactive whiteboard, emoticons, models of figures, development of figures, individual traffic lights, rectangles - means of feedback, Explanatory dictionary.

Lesson type: learning new material.

Methods: verbal, research, visual, practical.

Forms of work: frontal, group, pair, individual.

1. Organization of the beginning of the lesson.

In the morning the sun rose.
A new day has been brought to us.
Strong and kind
We are celebrating a new day.
Here are my hands, I open them
Them towards the sun.
Here are my legs, they are firm
They stand on the ground and lead
Me on the right path.
Here is my soul, I reveal
Her towards people.
Come, new day!
Hello new day!

2. Updating knowledge.

Let's create a good mood. Smile at me and at each other, sit down!

To reach your goal, you must first go.

There is a statement in front of you, read it. What does this statement mean?

(To achieve something, you need to do something)

And indeed, guys, only those who prepare themselves to be collected and organized in their actions can hit the target. And so I hope that you and I will achieve our goal in this lesson.

Let's begin our journey to achieving the goal of today's lesson.

3. Preparatory work.

Look at the screen. What do you see? ( Geometric figures)

Name these figures.

What task can you offer to your classmates? (divide the shapes into groups)

You have cards with these figures on your desks. Complete this task in pairs.

On what basis did you divide these figures?

• Flat and volumetric figures
• Based on volumetric figures

What figures have we already worked with? What did you learn to find from them? What figures do we encounter for the first time in geometry?

What is the topic of our lesson? (The teacher adds words on the board: volumetric, the topic of the lesson appears on the board: Volumetric geometric shapes.)

What should we learn in class?

4. “Discovery” of new knowledge in practical research work.

(The teacher shows a cube and a square.)

How are they similar?

Can we say that these are the same thing?

What is the difference between a cube and a square?

Let's do an experiment. (Students receive individual figures - cube and square.)

Let's try to attach the square to the flat surface of the port. What do we see? Did he lay down (entirely) on the surface of the desk? Close?

! What do we call a figure that can be placed entirely on one flat surface? (Flat figure.)

Is it possible to press the cube completely (entirely) to the desk? Let's check.

Can a cube be called a flat figure? Why? Is there space between your hand and the desk?

! So what can we say about the cube? (Occupies a certain space, is a three-dimensional figure.)

CONCLUSIONS: What is the difference between flat and three-dimensional figures? (The teacher posts conclusions on the board.)

• Can be placed entirely on one flat surface.

VOLUMETRIC

• occupy a certain space,
• rise above a flat surface.

Volumetric figures: pyramid, cube, cylinder, cone, ball, parallelepiped.

4. Discovery of new knowledge.

1. Name the figures shown in the picture.

What shape do the bases of these figures have?

What other shapes can be seen on the surface of a cube and a prism?

2. Figures and lines on the surface of volumetric figures have their own names.

Suggest your names.

The sides that form a flat figure are called faces. And the lateral lines are the ribs. The corners of polygons are vertices. These are elements of volumetric figures.

Guys, what do you think, what are the names of such three-dimensional figures that have many sides? Polyhedra.

Working with notebooks: reading new material

Correlation between real objects and volumetric bodies.

Now select for each object the three-dimensional figure that it resembles.

The box is a parallelepiped.

• An apple is a ball.
• Pyramid - pyramid.
• The jar is a cylinder.
• Flower pot - cone.
• The cap is a cone.
• The vase is a cylinder.
• The ball is a ball.

5. Physical exercise.

1. Imagine a big ball, stroke it from all sides. It's big and smooth.

(Students “wrap” their hands around and stroke an imaginary ball.)

Now imagine a cone, touch its top. The cone grows upward, now it is already taller than you. Jump to the top of it.

Imagine that you are inside a cylinder, pat its upper base, stomp on the lower one, and now with your hands along the side surface.

The cylinder became a small gift box. Imagine that you are a surprise that is in this box. I press the button and... a surprise pops out of the box!

6. Group work:

(Each group receives one of the figures: a cube, a pyramid, a parallelepiped. The children study the resulting figure, and write down the conclusions on a card prepared by the teacher.)
Group 1.(To study the parallelepiped)

Group 2.(For studying the pyramid)

Group 3.(For studying the cube)

7. Crossword solution

8. Lesson summary. Reflection of activity.

Crossword solution in presentation

What new things have you discovered for yourself today?

All geometric shapes can be divided into three-dimensional and flat.

And I learned the names of volumetric figures

Lesson topic

Geometric figures

What is a geometric figure

Geometric figures are a collection of many points, lines, surfaces or bodies that are located on a surface, plane or space and form a finite number of lines.

The term “figure” is to some extent formally applied to a set of points, but as a rule, a figure is usually called a set that is located on a plane and is limited by a finite number of lines.

A point and a straight line are the basic geometric figures located on a plane.

The simplest geometric figures on a plane include a segment, a ray and a broken line.

What is geometry

Geometry is like this mathematical science, which studies the properties of geometric shapes. If we literally translate the term “geometry” into Russian, it means “land surveying,” since in ancient times the main task of geometry as a science was the measurement of distances and areas on the surface of the earth.

The practical application of geometry is invaluable at all times and regardless of profession. Neither a worker, nor an engineer, nor an architect, nor even an artist can do without knowledge of geometry.

In geometry there is a section that deals with the study of various figures on a plane and is called planimetry.

You already know that a figure is an arbitrary set of points located on a plane.

Geometric figures include: point, straight line, segment, ray, triangle, square, circle and other figures that planimetry studies.

Dot

From the material studied above, you already know that the point refers to the main geometric figures. And although this is the smallest geometric figure, it is necessary for constructing other figures on a plane, drawing or image and is the basis for all other constructions. After all, the construction of more complex geometric figures consists of many points characteristic of a given figure.

In geometry, points represent in capital letters Latin alphabet, for example, such as: A, B, C, D....

Now let's summarize, and so, from a mathematical point of view, a point is such an abstract object in space that does not have volume, area, length and other characteristics, but remains one of the fundamental concepts in mathematics. A point is a zero-dimensional object that has no definition. According to Euclid's definition, a point is something that cannot be defined.

Straight

Like a point, a straight line refers to figures on a plane, which has no definition, since it consists of an infinite number of points located on one line, which has neither beginning nor end. It can be argued that a straight line is infinite and has no limit.

If a straight line begins and ends with a point, then it is no longer a straight line and is called a segment.

But sometimes a straight line has a point on one side and not on the other. In this case, the straight line turns into a beam.

If you take a straight line and put a point in its middle, then it will split the straight line into two oppositely directed rays. These rays are additional.

If in front of you there are several segments connected to each other so that the end of the first segment becomes the beginning of the second, and the end of the second segment becomes the beginning of the third, etc., and these segments are not on the same straight line and when connected have a common point, then such the chain is a broken line.

Exercise

Which broken line is called unclosed?
How is a straight line designated?
What is the name of a broken line that has four closed links?
What is the name of a broken line with three closed links?

When the end of the last segment of a broken line coincides with the beginning of the 1st segment, then such a broken line is called closed. An example of a closed polyline is any polygon.

Plane

Like a point and a straight line, a plane is a primary concept; it has no definition and one cannot see either a beginning or an end. Therefore, when considering a plane, we consider only that part of it that is limited by a closed broken line. Thus, any smooth surface can be considered a plane. This surface can be a sheet of paper or a table.

Corner

A figure that has two rays and a vertex is called an angle. The junction of the rays is the vertex of this angle, and its sides are the rays that form this angle.

Exercise:

1. How is an angle indicated in the text?
2. What units can you use to measure an angle?
3. What are the angles?

Parallelogram

A parallelogram is a quadrilateral whose opposite sides are parallel in pairs.

Rectangle, square and rhombus are special cases of parallelogram.

A parallelogram with right angles equal to 90 degrees is a rectangle.

A square is the same parallelogram; its angles and sides are equal.

As for the definition of a rhombus, it is a geometric figure whose all sides are equal.

In addition, you should know that every square is a rhombus, but not every rhombus can be a square.

Trapezoid

When considering a geometric figure such as a trapezoid, we can say that, in particular, like a quadrilateral, it has one pair of parallel opposite sides and is curvilinear.

Circle and circle

Circle - the geometric locus of points in the plane equidistant from given point, called the center, to a given non-zero distance, called its radius.

Triangle

The triangle you have already studied also belongs to simple geometric figures. This is one of the types of polygons in which part of the plane is limited by three points and three segments that connect these points in pairs. Any triangle has three vertices and three sides.

Exercise: Which triangle is called degenerate?

Polygon

Polygons include geometric shapes different forms, which have a closed broken line.

In a polygon, all points that connect the segments are its vertices. And the segments that make up a polygon are its sides.

Did you know that the emergence of geometry goes back centuries and is associated with the development of various crafts, culture, art and observation of the surrounding world. And the name of geometric figures is confirmation of this, since their terms did not arise just like that, but due to their similarity and similarity.

After all, the term “trapezoid” translated from the ancient Greek language from the word “trapezion” means table, meal and other derivative words.

“Cone” comes from the Greek word “konos,” which means pine cone.

“Line” has Latin roots and comes from the word “linum”, translated it sounds like linen thread.

Did you know that if you take geometric figures with the same perimeter, then among them the circle turns out to have the largest area.

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Introduction

Geometry is one of the most important components of mathematical education, necessary for the acquisition of specific knowledge about space and practically significant skills, the formation of a language for describing objects in the surrounding world, for the development of spatial imagination and intuition, mathematical culture, as well as for aesthetic education. The study of geometry contributes to the development of logical thinking and the formation of proof skills.

The 7th grade geometry course systematizes knowledge about the simplest geometric figures and their properties; the concept of equality of figures is introduced; the ability to prove the equality of triangles using the studied signs is developed; a class of problems involving construction using a compass and ruler is introduced; one of the most important concepts is introduced - the concept of parallel lines; new interesting and important properties of triangles are considered; one of the most important theorems in geometry is considered - the theorem on the sum of the angles of a triangle, which allows us to classify triangles by angles (acute, rectangular, obtuse).

During classes, especially when moving from one part of the lesson to another, changing activities, the question arises of maintaining interest in classes. Thus, relevant The question arises about using tasks in geometry classes that involve the condition of a problem situation and elements of creativity. Thus, purpose This study is to systematize tasks of geometric content with elements of creativity and problem situations.

Object of study: Geometry tasks with elements of creativity, entertainment and problem situations.

Research objectives: Analyze existing geometry tasks aimed at developing logic, imagination and creative thinking. Show how you can develop interest in a subject using entertaining techniques.

Theoretical and practical significance of the research is that the collected material can be used in the process additional classes in geometry, namely at olympiads and geometry competitions.

Scope and structure of the study:

The study consists of an introduction, two chapters, a conclusion, a bibliography, contains 14 pages of main typewritten text, 1 table, 10 figures.

Chapter 1. FLAT GEOMETRIC FIGURES. BASIC CONCEPTS AND DEFINITIONS

1.1. Basic geometric figures in the architecture of buildings and structures

In the world around us, there are many material objects of different shapes and sizes: residential buildings, machine parts, books, jewelry, toys, etc.

In geometry, instead of the word object, they say geometric figure, while dividing geometric figures into flat and spatial. In this work we will consider one of the most interesting sections of geometry - planimetry, which considers only flat figures. Planimetry(from Latin planum - “plane”, ancient Greek μετρεω - “measure”) - a section of Euclidean geometry that studies two-dimensional (single-plane) figures, that is, figures that can be located within the same plane. A flat geometric figure is one in which all points lie on the same plane. Any drawing made on a sheet of paper gives an idea of ​​such a figure.

But before considering flat figures, it is necessary to get acquainted with simple but very important figures, without which flat figures simply cannot exist.

The simplest geometric figure is dot. This is one of the main figures of geometry. It is very small, but it is always used to build various shapes on a plane. The point is the main figure for absolutely all constructions, even the highest complexity. From a mathematical point of view, a point is an abstract spatial object that does not have such characteristics as area or volume, but at the same time remains a fundamental concept in geometry.

Straight- one of the fundamental concepts of geometry. In a systematic presentation of geometry, a straight line is usually taken as one of the initial concepts, which is only indirectly determined by the axioms of geometry (Euclidean). If the basis for constructing geometry is the concept of distance between two points in space, then a straight line can be defined as a line along which the path is equal to the distance between two points.

Straight lines in space can occupy different positions; let’s consider some of them and give examples found in the architectural appearance of buildings and structures (Table 1):

Table 1

Parallel lines	Properties of parallel lines
	If the lines are parallel, then their projections of the same name are parallel:	Essentuki, mud bath building (photo by the author)
Intersecting lines	Properties of intersecting lines	Examples in the architecture of buildings and structures
	Intersecting lines have a common point, that is, the intersection points of their projections of the same name lie on a common connection line:	"Mountain" buildings in Taiwan https://www.sro-ps.ru/novosti_otrasli/2015_11_11_pervoe_zdanie_iz_grandioznogo_proekta_big_v_tayvane
Crossing lines	Properties of skew lines	Examples in the architecture of buildings and structures
	Straight lines that do not lie in the same plane and are not parallel to each other are intersecting. None is a common communication line. If intersecting and parallel lines lie in the same plane, then intersecting lines lie in two parallel planes.	Robert, Hubert - Villa Madama near Rome https://gallerix.ru/album/Hermitage-10/pic/glrx-172894287

1.2. Flat geometric shapes. Properties and Definitions

Observing the forms of plants and animals, mountains and river meanders, landscape features and distant planets, man borrowed from nature its correct forms, sizes and properties. Material needs prompted people to build houses, make tools for labor and hunting, sculpt dishes from clay, and so on. All this gradually contributed to the fact that man came to understand the basic geometric concepts.

Quadrilaterals:

Parallelogram(ancient Greek παραλληλόγραμμον from παράλληλος - parallel and γραμμή - line, line) is a quadrilateral whose opposite sides are pairwise parallel, that is, they lie on parallel lines.

Signs of a parallelogram:

A quadrilateral is a parallelogram if one of the following conditions is met: 1. If in a quadrilateral the opposite sides are pairwise equal, then the quadrilateral is a parallelogram. 2. If in a quadrilateral the diagonals intersect and are divided in half by the point of intersection, then this quadrilateral is a parallelogram. 3. If two sides of a quadrilateral are equal and parallel, then this quadrilateral is a parallelogram.

A parallelogram whose angles are all right angles is called rectangle.

A parallelogram in which all sides are equal is called diamond

Trapezoid— It is a quadrilateral in which two sides are parallel and the other two sides are not parallel. Also, a trapezoid is a quadrilateral in which one pair of opposite sides is parallel, and the sides are not equal to each other.

Triangle is the simplest geometric figure formed by three segments that connect three points that do not lie on the same straight line. These three points are called vertices triangle, and the segments are sides triangle. It is precisely because of its simplicity that the triangle was the basis of many measurements. Land surveyors in their calculations of areas land plots and astronomers use the properties of triangles to find distances to planets and stars. This is how the science of trigonometry arose - the science of measuring triangles, of expressing the sides through its angles. The area of ​​any polygon is expressed through the area of ​​a triangle: it is enough to divide this polygon into triangles, calculate their areas and add the results. True, it was not immediately possible to find the correct formula for the area of ​​a triangle.

The properties of the triangle were especially actively studied in the 15th-16th centuries. Here is one of the most beautiful theorems of that time, due to Leonhard Euler:

A huge amount of work on the geometry of the triangle, carried out in the XY-XIX centuries, created the impression that everything was already known about the triangle.

Polygon - it is a geometric figure, usually defined as a closed polyline.

Circle- the geometric locus of points in the plane, the distance from which to a given point, called the center of the circle, does not exceed a given non-negative number, called the radius of this circle. If the radius is zero, then the circle degenerates into a point.

There are a large number of geometric shapes, they all differ in parameters and properties, sometimes surprising with their shapes.

In order to better remember and distinguish flat figures by properties and characteristics, I came up with a geometric fairy tale, which I would like to present to your attention in the next paragraph.

Chapter 2. PUZZLES FROM FLAT GEOMETRIC FIGURES

2.1.Puzzles for constructing a complex figure from a set of flat geometric elements.

After studying flat shapes, I wondered if there were any interesting problems with flat shapes that could be used as games or puzzles. And the first problem I found was the Tangram puzzle.

This is a Chinese puzzle. In China it is called "chi tao tu", or a seven-piece mental puzzle. In Europe, the name “Tangram” most likely arose from the word “tan”, which means “Chinese” and the root “gram” (Greek - “letter”).

First you need to draw a 10 x 10 square and divide it into seven parts: five triangles 1-5 , square 6 and parallelogram 7 . The essence of the puzzle is to use all seven pieces to put together the figures shown in Fig. 3.

Fig.3. Elements of the game "Tangram" and geometric shapes

Fig.4. Tangram tasks

It is especially interesting to make “shaped” polygons from flat figures, knowing only the outlines of objects (Fig. 4). I came up with several of these outline tasks myself and showed these tasks to my classmates, who happily began to solve the tasks and created many interesting polyhedral figures, similar to the outlines of objects in the world around us.

To develop imagination, you can also use such forms of entertaining puzzles as tasks for cutting and reproducing given figures.

Example 2. Cutting (parqueting) tasks may seem, at first glance, to be quite diverse. However, most of them use only a few basic types of cuts (usually those that can be used to create another from one parallelogram).

Let's look at some cutting techniques. In this case, we will call the cut figures polygons.

Rice. 5. Cutting techniques

Figure 5 shows geometric shapes from which you can assemble various ornamental compositions and create an ornament with your own hands.

Example 3. Another interesting task that you can come up with on your own and exchange with other students, and whoever collects the most cut pieces is declared the winner. There can be quite a lot of tasks of this type. For coding, you can take all existing geometric shapes, which are cut into three or four parts.

Fig. 6. Examples of cutting tasks:

------ - recreated square; - cut with scissors;

Basic figure

2.2. Equal-sized and equally-composed figures

Let's consider another interesting technique for cutting flat figures, where the main “heroes” of the cuts will be polygons. When calculating the areas of polygons, a simple technique called the partitioning method is used.

In general, polygons are called equiconstituted if, after cutting the polygon in a certain way F into a finite number of parts, it is possible, by arranging these parts differently, to form a polygon H from them.

This leads to the following theorem: Equilateral polygons have the same area, so they will be considered equal in area.

Using the example of equipartite polygons, we can consider such an interesting cutting as the transformation of a “Greek cross” into a square (Fig. 7).

Fig.7. Transformation of the "Greek Cross"

In the case of a mosaic (parquet) composed of Greek crosses, the parallelogram of the periods is a square. We can solve the problem by superimposing a mosaic made of squares onto a mosaic formed with the help of crosses, so that the congruent points of one mosaic coincide with the congruent points of the other (Fig. 8).

In the figure, the congruent points of the mosaic of crosses, namely the centers of the crosses, coincide with the congruent points of the “square” mosaic - the vertices of the squares. By moving the square mosaic in parallel, we will always obtain a solution to the problem. Moreover, the problem has several possible solutions if color is used when composing the parquet ornament.

Fig.8. Parquet made from a Greek cross

Another example of equally proportioned figures can be considered using the example of a parallelogram. For example, a parallelogram is equivalent to a rectangle (Fig. 9).

This example illustrates the partitioning method, which consists in calculating the area of ​​a polygon by trying to divide it into a finite number of parts in such a way that these parts can be used to create a simpler polygon whose area we already know.

For example, a triangle is equivalent to a parallelogram having the same base and half the height. From this position the formula for the area of ​​a triangle is easily derived.

Note that the above theorem also holds converse theorem: if two polygons are equal in size, then they are equivalent.

This theorem, proven in the first half of the 19th century. by the Hungarian mathematician F. Bolyai and the German officer and mathematics lover P. Gerwin, can be represented in this way: if there is a cake in the shape of a polygon and a polygonal box of a completely different shape, but the same area, then you can cut the cake into a finite number of pieces (without turning them cream side down) that they can be placed in this box.

Conclusion

In conclusion, I would like to note that there are quite a lot of problems on flat figures in various sources, but those that were of interest to me were the ones on the basis of which I had to come up with my own puzzle problems.

After all, by solving such problems, you can not only accumulate life experience, but also acquire new knowledge and skills.

In puzzles, when constructing actions-moves using rotations, shifts, translations on a plane or their compositions, I got independently created new images, for example, polyhedron figures from the game “Tangram”.

It is known that the main criterion for the mobility of a person’s thinking is the ability, through reconstructive and creative imagination, to perform certain actions within a set period of time, and in our case, moves of figures on a plane. Therefore, studying mathematics and, in particular, geometry at school will give me even more knowledge to later apply in my future professional activities.

Bibliography

1. Pavlova, L.V. Non-traditional approaches to teaching drawing: tutorial/ L.V. Pavlova. - Nizhny Novgorod: NSTU Publishing House, 2002. - 73 p.

2. encyclopedic Dictionary young mathematician / Comp. A.P. Savin. - M.: Pedagogy, 1985. - 352 p.

3.https://www.srops.ru/novosti_otrasli/2015_11_11_pervoe_zdanie_iz_grandioznogo_proekta_big_v_tayvane

4.https://www.votpusk.ru/country/dostoprim_info.asp?ID=16053

Annex 1

Questionnaire for classmates

1. Do you know what a Tangram puzzle is?

2. What is a “Greek cross”?

3. Would you be interested to know what “Tangram” is?

4. Would you be interested to know what a “Greek cross” is?

22 8th grade students were surveyed. Results: 22 students do not know what “Tangram” and “Greek cross” are. 20 students would be interested in learning how to use the Tangram puzzle, consisting of seven flat figures, to obtain a more complex figure. The survey results are summarized in a diagram.

Appendix 2

Elements of the game "Tangram" and geometric shapes

Transformation of the "Greek Cross"

There are an infinite number of forms. Shape is the external outline of an object.

The study of shapes can begin from early childhood, drawing your child’s attention to the world around us, which consists of shapes (a plate is round, a TV is rectangular).

From the age of two, a child should know three simple shapes - a circle, a square, a triangle. At first he should just show them when you ask. And at three years old, you can already name them yourself and distinguish a circle from an oval, a square from a rectangle.

The more exercises a child does to consolidate shapes, the more new shapes he will remember.

The future first-grader must know all the simple geometric shapes and be able to make applications from them.

What do we call a geometric figure?

A geometric figure is a standard with which you can determine the shape of an object or its parts.

Figures are divided into two groups: flat figures, three-dimensional figures.

We call plane figures those figures that are located in the same plane. These include circle, oval, triangle, quadrangle (rectangle, square, trapezoid, rhombus, parallelogram) and all kinds of polygons.

Three-dimensional figures include: sphere, cube, cylinder, cone, pyramid. These are those shapes that have height, width and depth.

Follow two simple tips when explaining geometric shapes:

1. Patience. What seems simple and logical to us, adults, will seem simply incomprehensible to a child.
2. Try drawing shapes with your child.
3. A game. Start learning shapes in game form. Good exercises for consolidating and studying flat shapes are applications from geometric shapes. For voluminous ones, you can use ready-made store-bought games, and also choose applications where you can cut out and glue a voluminous shape.