Tổng hợp kiến thức về góc trong hình học chi tiết nhất

Angle is a basic mathematical knowledge that will be learned from elementary school and throughout high school, appearing in textbook exercises until exams. To help children master the knowledge of angles, the following article by Nguyễn Tất Thành will summarize fully and in the most detail.

What is an angle?

In geometry, shapes in mathematics have one thing in common: they all have angles. Depending on each shape, the way to determine and identify angles is different.

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What are the characteristics of angles?

An angle is known as a figure consisting of two rays sharing a common angle. In particular, the common angle of the two rays is the vertex of the angle, the two rays are the two sides of the angle.

Note: When two lines are parallel and do not intersect at any point, they still have an angle. The angle between them will be 0 and there will be no defined vertex.

What are the properties of angles?

• A ray is also an angle, the corresponding measurement is 0 degrees.
• If ray OA lies between Oz and Oy, then A lies in angle zOy

A is in angle zOy

• If ray Oa is between Ox and Oy, then angle xOa + angle aOy = angle xOy.
• The bisector of angle xOy corresponds to:

• Oa is between Ox and Oy (angle xOa + angle aOy = angle xOy)
• Two angles divided by equal rays (angle xOa = angle aOy).

Angle bisector xOy

• Two adjacent angles are two angles that have a common edge, the remaining two edges will lie on opposite half planes.
• Two complementary angles will have a total measure equal to a right angle.
• Two complementary angles whose total measure is equal to a straight angle.
• Two complementary angles are two angles that are both complementary and adjacent, the total measure of which is equal to the straight angle.
• Two opposing rays will form a straight angle.

Note: Lines that converge at a point will create pairs of two vertical angles with the same measure.

Unit of angle measurement in geometry

One of the characteristics you need to know when learning about angles is the unit of measurement. Specifically, angles in geometry will have the following units of measurement:

• Radian: This is the standard unit for measuring plane angles, has no specific quantity, and is the ratio of arc length to radius length. A straight angle is equal to π radians.
• Degree: This is the most common unit of measurement, symbol is °, a flat angle is equal to 180 degrees.

• 1 degree = 60 minutes. The symbol is ‘.
• 1 minute = 60 seconds. The symbol is “.

Summary of the most common types of angles in geometry

In geometry, there are basic types of angles but important knowledge that you need to understand as follows:

Right angle

Right angles are the easiest to identify, as well as the most common and used angles in plane geometry. A right angle has a measure of 90°.

In geometry, squares, right triangles, rectangles, trapezoids, and rhombus will have right angles.

Acute angle

An acute angle is an angle created from two straight lines that share a common intersection. Acute angle measurements are usually greater than 0° and less than 90°.

In geometry, acute angles are angles in any triangle or trapezoid. Everyone can use a vise ruler to accurately determine the geometric value of any geometry. In particular, an acute angle will be smaller than a right angle.

Obtuse angle

An obtuse angle is a very special angle, when it is created from 2 straight lines in the plane, sharing a common intersection. An obtuse angle will have a value greater than a right angle, less than the sum of the 3 angles in a specific triangle 90° > acute angle No plane geometry exists in obtuse angles.

Flat corner

This is an angle with a measure of 180°, meaning half a circle, created from 2 straight lines that share a common intersection.

How to determine the value of angles

To be able to determine the value of an angle, know how many degrees they have, and which angle they belong to will depend on each type of shape. Basically, there will be the following ways to determine:

Use properties of geometry

When determining angle values, you can rely on properties of geometry. For example, a square or rectangle has the property that the angle value is 90°, that is a right angle. Or a triangle will remember that the sum of the 3 angles in the triangle is always 180°.

Note: Depending on different geometries, or the assumptions of the given problem, the value of the remaining angles can be calculated.

Use a protractor or square

To be able to measure the value of angles, people often use a vise or protractor to know exactly.

In particular, the ruler has a semi-circular shape, on the ruler will record measurements from 0 – 180° in 2 opposite arcs to make angle measurement easy.

In every student’s ruler tool kit, there will be a complete protractor, vise or goniometer.

How to draw detailed corners

To help students better understand how to draw angles when learning geometry, below is an example:

For example: Given ray AB, draw angle BAC = m° ( 0

First, students will place the protractor so that its center coincides with point A on ray AB. At this point, ray AB will pass through the 0° line. Then draw the line AC through the m-degree line of the ruler.

Finally, on the given half-plane with edge AB, you only draw 1 ray AC such that BAC = m degrees.

Some common types of angle exercises

Regarding knowledge about angles, elementary school students will often encounter the following basic to advanced exercises:

Form 1: Read the name of the angle, write the angle symbol and count the angle

In this exercise, you need to use 3 letters to write angles: the middle letter is the vertex of the angle, the 2 letters on both sides and the middle letter are the names of the two rays sharing the same origin to form the 2 sides of the angle. . Above the 3-letter corner name will have the symbol ^.

In addition, to calculate the number of angles, you will apply the formula n.(n-1)/2. Where n is the number of rays.

For example: Observe the picture and then fill in the table:

Form 2: Exercises on angle definition

The content will be theoretically related, students will rely on the characteristics and properties of angles to answer the questions given.

For example: Fill in the blanks in the following statements:

a, The figure consists of two rays with common roots Ox and Oy which are…

Point O is…

The two rays Ox and Oy are…

b, Angle RST has a vertex of …., and two sides of …

c, Flat angle is…

Solution:

a, Angle xOy; top; two edges.

b,S; SR and ST.

c, An angle whose two sides are opposite rays.

Type 3: Identify acute angle – right angle – obtuse angle – flat angle

Just like the name of the exercise, the problem will give shapes corresponding to the angles. Ask them to recognize what angle it is?

The usual solution is to use a protractor to know how many degrees there are, from which you can deduce what angle it is?

Example: Determine what angle the following angles belong to? Acute angle, right angle or obtuse angle? Use a protractor to determine the measurements of those angles.

Prize:

Form 4: Measure – draw angles

This is a basic type of exercise, usually the problem will ask students to draw an angle corresponding to a specific angle measurement.

With this type of exercise, you only need to rely on the given angle measurements. Use a protractor and proceed easily.

Form 5: General knowledge

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This is the most common type of exercise. When the test will often combine many different types such as drawing angles, recognizing angles, calculating angle measures,…

With this type of exercise, children need to have a solid grasp of knowledge about angles, types of angles, how to draw and measure angles, etc. To be able to conquer them easily.

For example: Let three points A, B, C be collinear, with B being the point between the other two points. Please draw ray Bx so that . Can you tell me what the measure of angle xBC is?

Prize:

Exercises about corners for children to practice on their own

After understanding some basic theory about angles, below is a summary of some exercises about angles so your child can practice on their own:

Experience helps children learn angle math effectively

In math, angles are difficult knowledge for some children. Therefore, to help children learn, understand and practice effectively, here are some tips that parents can apply with their children:

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Specifically, with Nguyễn Tất Thành Math, children will learn and get acquainted with more than 60 topics, corresponding to 7 topics across the preschool and elementary school levels, including geometry. The content will be divided into 4 levels from basic to advanced, through which parents will easily choose the level that best suits their child’s learning ability.

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Help your child master basic knowledge about angles

For every new knowledge your child learns, make sure your child “learns as much as he can” to avoid the situation of “learning first and forgetting later”.

Therefore, with basic knowledge about this angle, parents need to make sure their children have a solid grasp of related content such as: Characteristics of angles, types of angles, common math forms, etc. To do To achieve this, you should test your child’s theory to see how firmly he or she grasps it, and from there, adjust, guide, and strengthen the weak areas right from the beginning.

Practice regularly with your baby

Learning along with practice is an important factor when children learn any knowledge, and angle math is no exception. Because once you have grasped the theory, if you don’t practice regularly, it’s easy to quickly forget, as well as not clearly understand the nature of angles.

Therefore, parents should let their children practice regularly. The practice here can come from learning more knowledge about the internet corner with your child, doing exercises in the textbook or practicing for exams, organizing related games, taking practical examples, participating in Participate in interactive activities on Nguyễn Tất Thành Math,…

Regular practice not only helps children understand knowledge, but also ensures better memory and comprehensive training of mathematical thinking ability.

See more: Simple way to calculate the radius of a circle and effective self-practice exercises

Conclude

Above is the knowledge about angles in geometry. From there, it can be seen that this is an important form of math in geometry, the higher the grade level, the more difficult the knowledge will be. Therefore, children should firmly grasp the basic, but important, knowledge above to support better learning.

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