Geometry is the mathematical study of shapes and patterns. It contains flat, two-dimensional area such as square and circle to the three-dimensional shapes like cubes and spheres. Before go through into this you have to learn basic geometrical objects which create those shapes. You can follow the below steps for easy learning of geometry
Recognize the symbols which are used in geometry-
At the very beginning, you must understand all the basic symbols of geometry. Learn what each of them means and being able to immediately recognize them will make things easier. Below some description is given-
- A small triangle refers to the properties of a triangle.
- A small angle shape means the properties of an angle.
- One horizontal line with a vertical line in the middle means that two lines are perpendicular to each other.
- Two vertical lines refer to two lines are parallel to each other.
- An equal sign with a squiggly line on top means that two shapes are congruent.
Understanding the properties of lines-
The straight line can be extended up to infinite direction. It has one dimension, length. Points that are on the same line are called collinear points. If two or many lines are overlapped with one another than its called intersection of lines. You must learn about all the basic concepts of line like the properties of parallel, perpendicular and intersect lines.
Gather knowledge on various types of angles-
You must learn all about the angles and its basic properties from your reference book. Angles has three types- obtuse, acute and right. When the angle is greater than 90 degree than its called obtuse, acute measures less than 90-degree angle. So, clarify angle knowledge is important for learning geometry
Identify the types of the triangle-
Triangle is another essential part of geometry. There are three types of triangles. They are scalene, isosceles, and equilateral.
- An isosceles triangle has, at least, two congruent sides and two congruent angles
- An equilateral triangle has three identical sides and three identical angles.
Knowing about this kind of triangle helps you to identify properties and postulates associated with them
Understanding the basic principle-
You must understand all the basic theorem of geometry like euclidean equations, Pythagorean theorem. This theorem allows you to calculate the length of the side of a right triangle if you know the lengths of the other two sides. It also helps you to prove or calculate any geometrical triangle theory.
Learn about complementary and supplementary angles-
Angles which are added together to make 90 degrees is called complementary angles and which make 180 degrees is called supplementary angles. You must learn all about this topic from a particular textbook.
Memorize the trigonometric ratio-
You can memorize the ratios by SOHCAHTOA. Which means the formulas of sine, cosine and tangent. Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, and Tangent = Opposite/Adjacent.
Learn Euclid's five postulates of geometry-
This five postulate helps you to learn and apply many geometrical concepts easily. Because this is the foundation of basic geometry which is given below-
- A straight line segment can be drawn joining any two points.
- Any straight line segment can be continued in either direction indefinitely in a straight line.
- A circle can be drawn around any line segment serving as the center point and the length of the line segment serving as the radius of the circle.
- All right angles are equal.
- Given a single line and a single point, only one line can be drawn directly through the point that will be parallel to the first line.
Also, you can follow some strategies for cutting a good figure in the geometry section of the math exam by following below tricks in your exam sheet
Strategies for cutting good marks in the geometry section-
- Read the question carefully- First of all, you must observe the questions carefully and read which portions are given and which portions will be calculated or proved.
- Draw the diagrams after understanding the question- Sometimes the problems given in the question doesn't consist of any diagram. You will have to draw a diagram to visualize the question and proof.
- Make sure to label everything very clearly based on the information provided.
- The clearer your diagram, the easier it will be to think through the proof
- Write some observation about given topics-
- Write down the relationships between various lines and angles that you can conclude based on your diagram and assumptions.
- Write down the givens in the problem. In any geometric proof, there is some information that is given by the problem. Writing them down first can help you think through the process needed for the proof.
- Write the proof according to the observation- When you are proving something in geometry, you have to give some statements about the shapes and angles, then prove why the statements are true. Sometimes it's easy to start from the end of the proof for correcting all over the theory about the geometrical interpretation.
- Select which theorem you have to follow- There are many individual theorems in geometry. Also, There are many properties of triangles, intersecting and parallel lines, and circles that are the basis for any theorems. You never deduce the whole theorem into the geometrical interpretation. You just follow the theorem statements and answer the problem according to the selected theorem
- Follow the steps in a logical fashion- You must give priority to the step flow of your answer according to the questions. Write down the reasons for each step. Add the given statements where they belong, not just all at once in the beginning. Re-order the steps if necessary.
- Write down the conclusion- The final steps you have to complete is a conclusion. You have to conclude your whole geometrical process in a single line or in a short paragraph. Once you have determined that the proof is sound, write QED at the bottom right corner to signify it is complete.
Why geometry is important?
Learning geometry is important because it can help you to discover patterns, areas, volumes, lengths and angles. Also, it provides you better understanding about all the objects around us.
If you want to gather much knowledge on geometry. Please check Best Geometry High School Books
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