Common Mistakes Made By Students In Similarity Of Triangles In CBSE Class 10
Students are always very serious about their class 10th boards, as it is the first important exam of their career. Now, the subject that students are most afraid of is mathematics. However, you should remember that math is a mark-fetching subject, and you must practice every chapter properly. But some chapters are very prone to common mistakes.
One of them is the similarity of triangles. So, if you are among those who don't like the chapter much and are sceptical about scoring well here, then this blog is for you.
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Overview
Students mostly lose marks for their silly mistakes and calculations. They tend to lose marks in this chapter, even though it is not that tough enough to score well in the chapter. Remember, this chapter can give you good marks if you know the right way to deliver your solutions. It can also boost your overall marks in the subject, which would guide you with the preparation of the chapter.
Why is the chapter important?
As far as the cbse board exam class 10 is concerned, the chapter triangle is very important. The chapter carries considerable weight in board exams, so skipping it is not an option at all. Students unknowingly make some mistakes or they could not frame their step-wise. This is the main reason why marks are deducted, and students tend to fear this chapter.
But if the above problem is taken care of, then the chapter will not bedifficult. It is possible to score well with proper practice. If you know the tricks and tips, then you may love the chapter. So, instead of skipping it, you should consider it of great importance.
How to understand triangles class 10?
Triangle is a time-consuming chapter but yet an important one. One of the major things about the chapter is its theorem, which is a bit scattered and confusing. So give yourself time to practice and learn those important triangle theorems and terms.
Once you are done with that, you can solve questions from NCERT books. Make sure to attempt all the questions that would make your concepts crystal clear. When you are done with NCERT, you can refer to other reference books and attempt questions from there. Remember to solve easy questions first; this will help boost your confidence.
Now comes the most important part: the PYQs. You just can't ignore this. Solve all important questions on the triangles class 10 cbse board exam. If you do something incorrectly or can’t find a solution, analyse your performance and work on it to improve.
Common mistakes made by students
Before proceeding, let us clarify the most common confusion, i.e. the difference between similar and congruent triangles. Congruent triangles are exactly the same in shape and size and completely overlap one another. However, similar triangles have the same shape, but their sizes can be enlarged or diminished compared to the other triangle.
- Not drawing a diagram with the correct naming
The first mistake that most students make is not drawing diagrams. When solving any geometry-related chapter, the most important step is the diagram. It helps you understand the question better and also leaves a good impression on the evaluator.
- Not to mention the information provided
Make sure you always write about what is given. It will ultimately help you grasp the question easily and without confusion. It will make the problem-solving process easier. Also, each step carries a mark so don't skip it.
- Naming the triangles correctly and writing the corresponding parts
Always name them carefully and correctly, since a wrong name can lead to wrong answers. Also, noting the corresponding parts is important.
For example, if T1 (the first triangle) is in the numerator and T2 (the second triangle) is the denominator, then all the corresponding parts of T1 will be in the numerator and the parts of T2 will be in the denominator.
- Not using C.P.S.T
For congruent triangles, C.P.C.T. is well known. Students tend to write C.P.C.T.(corresponding parts of a congruent triangle) while solving similar triangle problems. Remember to use C.P.C.T. for congruence and C.P.S.T. (corresponding parts of a similar triangle) for similarity.
- Skipping steps
In cbse board exams, marks are given on a step basis, and each step carries some marks. So skipping any step without giving a proper reason can cost you marks. Thus, to be on the safe side, don’t skip steps, and if you do, then do it with proper reasoning.
- Missing the similarity test
Never miss mentioning the similarity test that you have used, whether it is SSS, AA, AAA, or SAS. It can cost you marks.
Points to remember
- Two congruent triangles have an equal area
- Two similar triangles may or may not have an equal area
- Two similar triangles may or may not be congruent
- All congruent triangles are similar
- ASS or SSA is not similarity criteria
A Solved Example
Question: Sides AB and BC and the median AD of a triangle ABC are respectively proportional to sides PQ and QR and the median PM of ∆ PQR. Show that ∆ ABC ~ ∆ PQR
Solution: Given. AD and PM are the medians of ∆ABC and ∆PQR respectively
AB/PQ = BC/QR = AD/PM
To prove - ∆ ABC ~ ∆ PQR
Since AD and PM are medians so,
BD/QM = (BC/2)/(QR/2) = BC/QR
Now, in ΔABD and ΔPQM
AB/PQ = BD/QM = AD/PM
ΔABD ∼ ΔPQM (SSS criterion)
So, ∠ABC = ∠PQR (C.P.S.T)
Also, AB/PQ = BC/QR (Given)
Hence, ∆ ABC ~ ∆ PQR (SAS criteria)
Where to get practice questions?
Once you are done with your theory part, you must skip to the question banks to solve them. First of all, practice all the examples, exercises, and miscellaneous questions from the NCERT books more than once. After NCERT, you can refer to questions in other reference books and practice triangle chapter important questions from the internet.
In case you are not through with the theory part, you can find detailed notes on triangles on the Physics Wallah website. You can also find all formulas, NCERT solutions, and even extra questions and answers.
If you need further help, you can watch the video lectures of the chapters on the Physics Wallah youtube channel.
Conclusion
So, we have mentioned everything you need to know about the preparation of the triangles chapter, along with the common mistakes made by students. If you keep these things in mind and avoid making such common mistakes, you can score good marks in your board exams.
For notes and practice questions for the chapter, you can find them on the Physics Wallah official sites. If you still have further questions, don’t forget to ask us in the comment section.
Frequently Asked Questions (FAQs)
Q.1.What are the 4 tests for similar triangles?
Ans. The similarity criteria for triangles includes four tests-
- AAA: (Angle Angle Angle)
- SSS: (Side Side Side)
- SAS: (Side Angle Side)
- RHS: (Right angle- Hypotenuse-Side)
Q.2. Where can I get triangles chapter class 10 notes
Ans. Physics Wallah website can provide you with high-quality and precise notes on the chapter, along with extra questions to solve.
Q.3. Why is AAA not a theorem?
Ans. AAA is included as a theorem for the similarity of triangles but it is invalid for proving the congruence of triangles.
Q.4.Which chapter is most important for class 10 maths?
Ans. Linear Equations
- Coordinate Geometry
- Triangles
- Arithmetic Progressions
- Trigonometry