Why do you need a ruler: from simple measurements to improvised means. What is a protractor? Rules for measuring angles

A protractor is a geometric tool used to measure angles.

What does a protractor look like?

Each goniometric scale contains a line of angle values ​​in both the forward and reverse directions. This allows the protractor to be used to measure both acute and obtuse angles.

The materials used to make protractors can be very different. The most common options for such materials are plastic and metal. Wood is currently used somewhat less frequently for these purposes, since such protractors are usually thicker and somewhat less convenient to use.

The measurement accuracy of each instrument is directly dependent on its size. Thus, larger protractors allow you to measure angles with greater accuracy, but small instruments give only an approximate idea of ​​the size of the measured angle.

How to use a protractor

After this, you need to look at what value the side of the angle intersects the indicated scale. If an acute angle is being measured, the desired value will be less than 90°, and when measuring an obtuse angle, you should use that part of the scale that contains divisions exceeding 90°.

Angles are constructed in a similar way using a protractor. First, you should draw a line that will represent one of the sides, and place it, which will become the vertex, at the starting point. Then, on the goniometric scale, you need to mark the desired angle, which can be either acute or obtuse. After this, removing the protractor, connect the vertex of the future angle with the marked point: as a result, you will get the desired angle.

Every schoolchild knows what a protractor is. This seemingly unsightly tool performs very important functions not only in mathematics lessons. We will tell you further about what it is, as well as how to use it correctly.

What is a protractor?

A protractor is an object with which each of us can not only measure angles, but also construct them. Outwardly, it resembles a semicircular ruler with a scale and divisions. Below, on a flat surface, there is a straight ruler familiar to us for measuring segments. In the upper part there is a semicircle with a double scale for measurements. In each direction, the scale is distributed along the protractor from 0 to 180 degrees.

Terms of use

At school they explain what a protractor is in math lessons. This is where measurements are needed.

In order to find out what one degree is equal to, we need to divide the circle into 360 equal parts. One of these parts will be equal to 1 degree. The size of the circle will not affect the degree in any way! This is easy to check.

Let's draw two circles of different diameters and divide each into 360 equal parts. Then we will superimpose the smaller circle on the larger one and see that the lines coincide.

Measuring the angle

A protractor helps construct and measure an angle. A degree is a generally accepted unit used to measure angles. There are several types of angles:

• Spicy. This is called an angle of up to 90 degrees.
• A right angle is an angle equal to 90 degrees.
• The obtuse angle varies from 90 to 180 degrees.
• A straight angle is a straight line or 180 degrees.
• A full angle looks like a circle and is 360 degrees.

It's not difficult to figure out how to measure an angle. In order to find out what the size of the angle is, we need to install the protractor so that its center is located at the apex of the angle, and the straight side coincides with one of its sides. The scale will tell us the number of degrees of a given angle. In this simple way we can find out what is around the corner in front of us.

To construct an angle with a given degree, you should attach the straight part of the protractor to the line, and its center to the beginning of the line. Subsequently, this point will be the vertex of the angle. Then we find the given number on the scale and put a dot. Now the protractor can be removed and connected with a segment from the beginning of the line (vertex of the angle) to the marked point.

School stationery produced by different companies differs in material, color, and size. So: for those whose protractor turns out to be longer than the length of the angle, and it is not possible to determine its value, the side of the angle must be extended using a straight ruler.

Schoolboy set

It is no wonder that junior students are not familiar with the protractor. When using it, a certain knowledge base must be laid down. To fully work with it in class, children study a number of related subjects. Before learning what a protractor is, schoolchildren must master a straight ruler, draw straight lines, learn addition and subtraction, master a compass, know geometric figures, and so on. This entire process takes time, and it is only after graduating from primary school that a student can add a protractor to their toolbox.

Students are now offered a huge selection of school stationery. The protractor is no exception. Manufacturers try to satisfy the most demanding needs of customers. Tools are made in various colors. Children always like bright colors. Sometimes even in the same class you cannot find identical protractors, which makes it easier to find them if they are lost. Everyone chooses shapes and sizes to their own taste.

Most of these products are made of plastic, and this significantly reduces its cost. But there are wooden and even iron protractors. As practice shows, metal ones, although opaque, are more practical in the sense that the scale is not erased, and this allows you to use it in action for much longer, accurately determining angles.

The protractor is not as popular among schoolchildren as the ruler, but it accompanies students right up to the final exam. Some of the school's graduates choose specialties that involve measuring and constructing angles, designing buildings and structures, and working with drawings. Due to their professions, they constantly have to deal with protractors and its derivatives. But even former classmates of current engineers, sometimes even with the deepest humanitarian bias, can easily remember their skills in handling this subject and determine the number of degrees at any angle.

Bottom line

Today, modern children are accustomed to getting any information from the Internet. However, it will not help in measuring angles. Only the ability to use a protractor will make it possible to correctly identify them. Future engineers and designers will undoubtedly find this useful in their work, and every educated person should have the skills to work with protractors, so everyone should be able to use such a tool!

Let us conditionally distinguish two parts in the protractor - a “ruler”, also called a rectilinear scale (lower part in the figure), and a semicircle, also called a goniometer scale. On the semicircle there are degree marks from 0° to 180°. Let's call the division into degrees a “degree grid.”

Protractors come in different types, but their use comes down to the following. The protractor has a center mark. In the picture above it is a small circle with a hole in the center. However, the central mark may simply be indicated by a dash. This mark must be aligned with the top of the corner. In this case, one of the sides of the angle must pass through the mark with the number 0 on the semicircle of the protractor.

There can be two “zero” marks on the protractor: on the right and on the left. It is clear that you should look at the one through which the side of the corner passes. But the most important thing is to understand which degree grid to look at when measuring the angle: upper or lower. If the side of the angle passes through 0, which is located on the outside, then in the future we use the external degree grid. If the side of the angle passes through the “internal” 0, then in the future we use the internal degree grid of the protractor (we do not pay attention to the external one).

So, one side of the angle should pass through the 0 mark, and the second side of the angle should be on the side of the semicircle (goniometric scale), that is, as if intersecting it.

The magnitude of the angle is determined by the place where the second side of the angle intersects the protractor's goniometric scale.

Measuring an angle with a protractor

1. Evaluate what type of corner you are interested in. Angles can be divided into three classes: acute, obtuse and right.

   Acute angles are relatively narrow (less than 90 degrees), obtuse angles are wider (greater than 90 degrees), and right angles measure 90 degrees (their sides are perpendicular to each other). Evaluate by eye what type the angle you are about to measure belongs to. A preliminary assessment will help you determine the required range and select the correct protractor scale.
   At first glance, we can say that the image above shows an acute angle, that is, its value is less than 90 degrees.

2. Place the center of the protractor at the apex of the angle you are measuring. There is a small hole in the middle of the protractor. Place the protractor on the corner so that the hole lines up with the top of the corner.
3. Rotate the protractor so that one side of the angle aligns with the base of the tool. Slowly turn the protractor and make sure that the apex of the angle remains in the center. As a result, one of the sides of the angle should align with the base of the protractor.
   In this case, the second side of the angle must intersect the arc of the protractor (its rounded part).
4. Follow the second side of the angle that intersects the arc of the protractor. If the second side does not reach the arc of the tool, extend it. You can also attach a piece of paper to this side of the corner that would extend to the arc of the protractor. The number crossed will tell you the angle in degrees.
5. In the example above, the angle value is 70 degrees.

   protractor with ruler

   In this case, we use a smaller scale, since we determined earlier that we are dealing with an acute angle, that is, its value does not exceed 90 degrees. For obtuse angles, use a larger scale with values ​​greater than 90 degrees.

6. At first, you can get confused with the scale. Most protractors have two scales, one on the inside and one on the outside of the round part. This is done to make it convenient to measure angles of both left and right orientation.

It is enough to take ordinary school supplies - a pencil and paper, a ruler, a protractor and a compass - and you can draw any geometric figure, be it a square, an oval, a triangle. However, there are times when there are no drawing tools at hand at all or their number is limited, but even in this case you can make the necessary drawing.

You will need

• - ruler;
• - pencil;
• - paper;
• - compass;
• - protractor;
• - right triangles

Instructions

• If you have nothing at hand except a sheet of paper and a pencil, then you can get by with even these supplies. To do this, very carefully fold a sheet of paper in four, while smoothing the folds well. As a result, at the place of the double fold you will get a right angle that has 90°. Fold the corner in half again, and you get the desired angle of 45°. True, in this case a small error will appear in the form of a loss of several degrees. For a more accurate drawing, trace a right angle with a pencil onto a blank sheet of paper, carefully cut it out and fold it in half - this will give an angle of 45°.
• You can draw an angle using right triangles, which can be different - with angles of 90°, 45°, 45° and 90°, 60°, 30°. Take a triangle (with angles 90°, 45°, 45°) and trace an acute angle of 45° on a piece of paper. If there is only a triangle with angles of 90°, 60°, 30°, then on another sheet of paper draw a right angle, cut it out, fold it in half and trace it on the desired drawing. This will be an angle of 45°.
• The most accurate construction option would be one that uses a protractor. Draw a line on a piece of paper, mark a corner point on it, attach a protractor and mark a 45° point, then connect them together.
• Interestingly, even with the help of a compass you can also draw an angle of 45°. To do this, it is enough to have a depicted 90° angle in front of you (for example, using a right triangle or by folding the paper in four). Then draw a circle from the corner point with a compass.

  How to use a protractor correctly?

  At the intersection of the circle and the sides of the right angle, mark the points. Now, from each of the two points, use the same compass solution to make two more circles. At the place where they intersect, you will get a point, which you connect to the corner, resulting in two angles of 45°.

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Protractor

NOT. Zhukovsky Mathematics has its own beauty, just like painting and poetry.

What is a protractor? A protractor is a tool for constructing and measuring angles. The protractor consists of a ruler (straight-line scale) and a semicircle (protractor scale), divided into degrees from 0 to 180°.

presentation on the topic "Protractor", history and rules of use

In some models - from 0 to 360°. .

What are protractors made of? Protractors are made of steel, plastic, wood and other materials. .

History of the protractor History has not preserved the name of the scientist who invented the protractor - perhaps in ancient times this instrument had a completely different name. The modern name comes from the French word “TRANSPORTER”, which means “to carry”. Presumably, the protractor was invented in ancient Babylon. .

Types of protractors Semicircular (180 degrees) are the simplest and most ancient protractors. Circular (360 degrees). Geodesics, which come in two types: TG-A - for constructing and measuring angles on plans and maps; TG-B - for drawing points on a drawing basis at known angles and distances. The division value of the goniometric scale is 0.5°, the rectilinear scale is 1 millimeter. Improved types of protractors, which are necessary for more accurate constructions and measurements. For example, there are special protractors with a transparent ruler with a goniometric vernier, which rotates around the center. .

What is a protractor used for? A protractor is a tool widely used in geometry. At the same time, it is quite difficult to do without this tool both for schoolchildren solving their first problems and for engineers performing complex geometric constructions. Most often, a protractor is used to obtain the degree measure of an angle. Without a protractor, we will not be able to measure an angle. .

How to use a protractor? To measure an angle, you need to place its vertex at the origin point marked on the protractor ruler. Then you need to pay attention to the fact that the side of the angle directed to the goniometer scale intersects it. If the length of this side is insufficient, it should be extended until it intersects the goniometric scale. After this, you need to look at what value the side of the angle intersects the indicated scale. If an acute angle is being measured, the desired value will be less than 90°, and when measuring an obtuse angle, you should use that part of the scale that contains divisions exceeding 90°. Angles are constructed in a similar way using a protractor. First, you should draw a line that will represent one of the sides, and its end, which will become the vertex, should be placed at the starting point. Then, on the goniometric scale, you need to mark the desired angle, which can be either acute or obtuse. After this, removing the protractor, connect the vertex of the future angle with the marked point: as a result, you will get the desired angle. .

Thank you for your attention!

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Let's talk about what a ruler and protractor are for. These two useful tools are used not only in school during geometry and drawing lessons, but also in everyday life.

Purpose of the ruler

A ruler is a long narrow rectangular strip with a scale and numbers printed along the top edge (on some rulers and along the bottom edge).

Why does a person need a ruler? Firstly, for measuring small distances, lengths, heights and widths of various objects; secondly, to draw even straight lines using a pencil, pen, or felt-tip pen. That is, the ruler has two main functions: measuring and drawing straight lines. Often both are used at once, for example, you need to draw a rectangle with sides of 5 cm and 7 cm. Take a ruler, apply it to the sheet in the right place, first horizontally, draw from 0 to 7 cm with a pencil, then draw perpendicular sides at the ends of 5 cm each and complete the top side 7 cm.

On the other hand, the ruler is not used for constructions, but simply for measurements. For example, you need to measure the length of a pen to know whether it will fit into a miniature pencil holder or not.

Purpose of the protractor

Now let's talk about the purpose of the protractor and how to use it. In geometry and drawing, you often have to build lines at a certain angle. Without a tool, only three angles can be distinguished: 0 o - horizontal, 90 o - vertical, 180 o - adjacent (also horizontal, but on the other side of 0 o.

Above we figured out what the ruler is for. A protractor is also a useful and necessary item, but it is used very rarely in everyday life. In construction, for example, it is replaced by a level.

To construct an angle, for example, 75 o, you should attach the protractor to the desired line so that the upper part of its horizontal ruler lies on the drawn line. Then on the protractor scale we find 75 o. Place a dot next to the “75” mark, as well as a second dot in the center of the protractor ruler. That's it, connect two points and get a line at an angle of 75 degrees. This is why you need a ruler with a hole or mark in the center opposite 90 o on each protractor.

Where else are they used?

Very often, when carrying out repair work, compiling tables in magazines and notebooks, creating various products, craftsmen of various professions, housewives, and workers use this tool. Why does an accountant, for example, need a ruler? When entering data from sheets into the computer, it places a ruler on the line you need to work with. This way he won't lose where he left off.

These are the useful properties of a ruler and a protractor! And they are inexpensive and accessible to everyone.