AT Everyday life we are surrounded by many different things. Some of them have the same size and the same shape. For example, two identical sheets or two identical bars of soap, two identical coins, etc.
In geometry, figures that have the same size and shape are called equal figures. The figure below shows two figures A1 and A2. To establish the equality of these figures, we need to copy one of them onto a tracing paper. And then move the tracing paper and combine a copy of one shape with another shape. If they are combined, then this means that these figures are the same figures. When this is written A1 \u003d A2 using the usual equal sign.
Determining the equality of two geometric shapes
We can imagine that the first figure was superimposed on the second figure, and not its copy on the tracing paper. Therefore, in the future we will talk about imposing the figure itself, and not its copy, on another figure. Based on the foregoing, we can formulate the definition equality of two geometric shapes .
Two geometric figures are called equal if they can be combined by superimposing one figure on another. In geometry, for some geometric shapes (for example, triangles), special signs are formulated, upon fulfillment of which we can say that the figures are equal.
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In this problem, we need to understand the concept of equality of figures.
Geometric figure
Let's understand the concept of a geometric figure. To do this, we introduce a definition.
Definition: A geometric figure is 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.
Equal figures
- Geometric figures will be called if they have the same shape, dimensions, their areas and perimeters are equal;
- For example, the length of the square is 4 cm. The area of the square can be found by following formula: S = a^2 = 16 cm^2. The width of the rectangle is 2 cm and its length is 8 cm. The area of the rectangle can be found using the following formula: S = a * b = 2 * 8 = 16 cm^2. The areas of the two figures are equal. But the figures themselves will not be equal, because they have a different shape;
- If you take two circles, it is obvious that their shapes are equal. But if they have different radii, but the figures will not be equal;
- Equal figures will be called two squares with equal sides, two circles with the same radius.
"The cylinder is called the body"- The section of a cylinder by a plane passing through the axis of the cylinder is called an axial section. A cylinder, an axial section whose square is called equilateral. Project "Mathematics in the profession "Cook, confectioner". Task number 3. Cylinders. The height of a cylinder is the distance between the planes of the bases. The height of the cylinder is 8 m, the radius of the base is 5 m. The cylinder is crossed by a plane so that the cross section is a square.
"Squares of figures geometry"- Equal figures have equal areas. in). what will be the area of the figure composed of figures A and D. The figures are divided into squares with a side of 1 cm. Equal figures b). The area of a parallelogram. Figures with equal areas are called equal areas. Areas of various figures. Area units. Area of a triangle.
"Areas of figures" - The area of a triangle. The area of a plane figure is non-negative number. Let S be the area of triangle ABC. Solution: Theorem: Area of a parallelogram. Decision. The area of a square with side 1 is equal to 1. Problem. Cutting and folding. Equal polygons have equal areas. Fourth property: The theorem is proved.
"Construction of Geometric Figures"- Methods of image and construction of spatial figures on the plane. Buildings on the projection drawing. P4: Construct (find) the point of intersection of the given line and circle. Requirements - the desired figure (set of figures) with specified properties. Algebraic Method. Stages of solving construction problems.
"Geometric progression" - 1073741823 > 3000000, so the merchant lost! Geometric progression. The infinite sum turned out to be equal to a completely finite value - the height of the triangle. Property geometric progression: Problem solution: b1 = 1, q =2, n =30. Bn = b1 · qn – 1 is the formula of the nth member of the progression. The formula for the sum of an infinite decreasing geometric progression:
"Similar figures"- Plants. Geometry. Similarity surrounds us. Toys. similarity in our lives. Here are some examples from our life. If you change (increase or decrease) all the dimensions of a flat figure by the same number of times (similarity ratio), then the old and new figures are called similar. Internet materials were used.
Plane figures with the same area or geometric bodies with the same size... Big Encyclopedic Dictionary
Plane figures with the same areas or a geometric body with the same volumes. * * * EQUAL-VALUE FIGURES EQUAL-VALUE FIGURES, flat figures with the same areas or geometric bodies with the same volumes ... encyclopedic Dictionary
Plane figures with the same area or geome. bodies with the same volume... Natural science. encyclopedic Dictionary
Equal-sized figures are flat (spatial) figures of the same area (volume); equally composed figures of a figure that can be cut into the same number of respectively congruent (equal) parts. Usually the concept... Great Soviet Encyclopedia
Two figures in R2 having equal areas and, respectively, two polygons M1 and M 2 such that they can be cut into polygons so that the parts that make up M 1 are respectively congruent to the parts that make up M 2. For, equal area ... ... Mathematical Encyclopedia
EQUAL, oh, oh; ik. 1. Equal in strength, capabilities, value (book). Equivalent phenomena. 2. equal-sized figures (bodies) in mathematics: figures (bodies) that are equal in area or volume. | noun equivalence, and, wives. Dictionary Ozhegova. ... ... Explanatory dictionary of Ozhegov
Here are collected definitions of terms from planimetry. References to terms in this dictionary (on this page) are in italics. # A B C D E F F G I K L M N O P R S ... Wikipedia
Here are collected definitions of terms from planimetry. References to terms in this dictionary (on this page) are in italics. # A B C D E F G I J K L M N O P R S T U V ... Wikipedia
