How To Learn Geometry

On Nov 19, 2020

Mathematics is not interesting for most of us, and one of the prime reasons is geometry. But none of us can argue on the point that geometry acts as the building blocks of mathematics and is a fundamental concept if you want to excel in the subject. Though many students feel that geometry is difficult, if you study and learn it properly, it is one of the easiest and most high scoring chapters in mathematics. So, here we present the proper way to study and learn geometry.

Draw diagrams

Geometry is all about points, lines, angles, and different shapes. So, it is imperative to practice geometry practically by drawing diagrams. Though mental maths ability which includes solving problems in mind, is very much needed in Geometry but solely relying on it is not a proper way of learning mathematics.

First of all, read the whole question properly and then start picturing it in the form of a diagram as this will help you understand the question better. A lot of doubts regarding the question get answered once you start making a diagram. This method will definitely help you score well in Geometry exams.

Remember all theorems and properties by heart

Geometry has a lot of theorems and properties; those are imperative to solve geometry problems, form relationships, and even in understanding questions. Knowing all properties and theorems of different shapes and angles will help you solve the question quickly. It is very important to learn the following:

Theorems related to triangles and angles
Properties of different shapes and lines

Here are a few theorems for triangles that are often asked in exams and are very important to solve various problems that are as follows:

SSS or Side Side Side: If all 3 sides of 2 different triangles are of equal length, both the triangles are congruent to each other.
SAS or Side Angle Side: If 2 sides of 2 different triangles are of the same length and the angles between them are also congruent, both the triangles are congruent to each other.
ASA or Angle Side Angle: If 2 different triangles have 1 line of the same length and the 2 angles formed by the lines are also congruent, both the triangles are congruent to each other.
HL or Hypotenuse Leg: This theorem only applies to right-angled triangles. It states that if the Hypotenuse and at least one side of 2 different right-angled triangles are of the same length, the 2 triangles are congruent to each other.
AAA or Angle Angle Angle: It states that if 2 different triangles have equal angles, those triangles are similar but may or may not be congruent.

Understanding and revising Euclid’s postulates:

Knowing and remembering all of Euclid’s postulates will help you understand many important geometry concepts. Euclid gave 5 postulates which are as follows:

1. Two points form a line segment: Joining 2 points allows you to form a straight line segment.
2. A line has infinite length: A line can be extended in any direction to an infinite length.
3. Any line segment can be converted into a radius of a circle by drawing a circle using that line segment.
4. All right angles are perpendicular, that is they are of 90°.
5. If the inner angles of 2 line segments are less than 180° such that a third line segment intersects 2 line segments, the line segments must intersect each other when extended.

Understand the language of maths

Maths is just like English or any other language which does have its own symbols, signs, and ways of communicating. All the symbols of mathematics signify some definitions, properties, and words. A maths student needs to understand these symbols; otherwise, you will definitely face a problem in geometry. Some commonly used symbols are to show if 2 lines are parallel, perpendicular, and congruent to each other. There are symbols even to show if AB is a line, line segment, or a ray. You can try writing these symbols every day to remember them.

Learn angles

Angles are the basics of geometry, and they are really important if you want to learn and study geometry. Angles help in making diagrams, understanding questions, and even understanding shapes. So, here are all the angles and their measurements as follows:

Acute angles are those angles that measure less than 90°.
Right angles are those angles that are exactly 90°.
All angles that are greater than 90° but less than 180° are called Obtuse angles.
Straight angles are those angles that are exactly 180°.
Angles that measure greater than 180° but less than 360° are called Reflex angles.
Complete angles are angles that are exactly 360°.
Knowing these angles will definitely help you in forming relationships among shapes and understanding problems.

Understanding triangles

3 types of triangles are used in geometry and often feature in questions are as follows:

Scalene triangles are triangles which do not have any sides and angles of equal length and measurement. The longest side of a scalene triangle is one opposite to the largest angle of the triangle, and similar is the case with the smallest side.
Equilateral triangles are triangles in which all sides are of equal length.
Isosceles triangles are triangles which have at least 2 equal angles and sides.
You can easily study these triangles by solving questions regularly and remembering the properties of all the triangles.

Always differentiate between what you need to prove and what is already given in the question

It is always advisable to read geometry questions at least twice to fully comprehend the question and find out what is asked to prove in the question and what is already given or stated in it. Realising this will provide you with a starting point that means the information already given the statement and help you reach the endpoint that is what you need to prove. It is just like using maps to find the best route where you already know the starting location and the destination. So, the best possible way to perform this is by writing a given statement where you write what information is already given and a ‘to prove’ statement where you mention what you are required to do or prove.

Start the proof process

Once you have written the given and to prove statements, you can start your proofing process by filling the missing information in the diagram and then using different properties, theorems, and postulates to prove your statement. The most important tip is to never assume anything until and unless it is mentioned in the question or is clearly visible in the diagram. Though the process of proofing is always difficult, regular practice and understanding of everything mentioned above will make the task easier for you. Now that you know the best way of learning and studying geometry, one often makes some common mistakes when solving geometry questions.

Common mistakes that you should avoid while performing geometry problems

Don’t confuse between congruent and similar: Similar means that 2 figures are of the same shape but may or may not be of the same size, while congruent means that 2 figures are completely identical which means they have equal sides, angles, and shape. All congruent figures are similar, but the opposite may or may not be true.

Don’t confuse between supplementary and complementary angles: Complementary angles are angles which, when added together, measure 90°, while supplementary angles are angles which, when added together, measure 180°. It is always better to understand the concept of transversal lines, parallel lines, vertical angles, alternate pair of interior angles, and alternate pair of exterior angles.

Never assume anything until or unless given in the problem: As already mentioned, a lot of students start assuming while solving geometry problems which leads to wrong answers. Geometry solutions should be based on principles, theorems, and properties, and no information other than what is given should be assumed. Forming diagrams will help you gain some extra information about the problem and help you avoid staying away from assumptions.

These were a few of the common mistakes that geometry students often make. Since you know about these mistakes now, we expect you to work on them and avoid them in your exams.

Conclusion

Now, start practising regularly, and soon, you will ace every problem with great ease. Don’t forget to form diagrams, remember all theorems and properties, and remember not to assume anything as it will affect your solution. If you need any other Geometry Tips and Tricks, you can always head to Cuemaths whose Geometry Tips and Tricks will help you solve problems quickly and score better in geometry. Their tips and tricks will make geometry and maths even more fun and exciting. If you have any questions or queries related to geometry and how to learn the subject, you can write in the comments section below.