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Parallel Lines: A fundamental portion of constructive Mathematics




Parallel lines are an intriguing part of Mathematics that helps a student in resolving the different complex problems. If one knows the importance of parallel lines, then one should also be familiar with their definition. Parallel lines are two or more lines that do not intersect each other even when extended indefinitely. If two or three parallel lines pass through the same point, they are called ‘parallel’.It is easy to define parallel planes too. Parallel planes cut each other such that they never meet.

To sum up, parallel lines are two or more straight lines that have the same direction and do not cross each other on a plane even though they continue indefinitely in both directions. This is because parallel lines remain parallel all through their course. Also, a line and a plane can be defined as parallel if they do not intersect each other at all.

Parallel lines cut a plane into two separate, non-overlapping regions called ‘parallel planes’. If one has ever used a divider to draw the boundary line between these two regions, then they can imagine that there is a hidden line that separates them. That is true but it cannot be seen because it remains parallel to the plane that contains it. To prove this fact, one can find a straight ray and draw a line on either side. It will be noticed that both of the lines keep going in the same direction forever, even if they are drawn as far as possible. It is due to this property that three or more parallel lines are capable of cutting an infinite plane into several infinite regions.

This article describes the various important properties associated with this crucial topic. It will help in clearing any doubts related to this portion.

Fundamental aspects associated with parallel lines:

  • The first and foremost property of parallel lines is that they never meet each other under any condition. Even if they are extended as far as possible in both directions, they will remain parallel to each other. This is the reason why two straight lines are also called ‘parallel’. A plane can be divided into infinite regions by three non-parallel lines. It is due to this property that parallelism is also called ‘lack of crossing’.
  • The second property of parallel lines is that they remain the same both vertically and horizontally. This helps a student draw parallel lines on a paper or any other plane without worrying about their direction. For example, lines which are parallel to the x-axis will be parallel to the y-axis. Furthermore, if one can draw two parallel lines on your paper then they can also find their equidistance very easily. They just have to start at one end of the line and keep moving in either direction without turning back. The distance between these two lines will remain the same all through the trip.
  • The third property states that only one line can be drawn through a given point. However, it does not mean that a line cannot be extended beyond a point. A line can be extended to infinity in both directions.
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This article is an attempt to cover all the important properties that are related to the lines that share a parallel relation between each other. They form a very crucial part of geometry. Students can seek the assistance of Cuemath to solve all the questions related to this important topic. It is an excellent platform that is being recommended by all the teachers because of its efficiency in dealing with problems of any kind. This is the reason why numerous students use this recognized platform.

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Benefits of Early Childhood Education



Early Childhood Education

Young children have a lot of creative thoughts which always whirl in their minds and make them do tremendous things. Their curiosity and imagination make them researcher from their childhood. They always keep searching things and ask questions about whatever they see around them. This curious nature of them always makes them search and find new things which can enhance their knowledge level and information too. It is therefore correct to say that early childhood education years are those years when these kids should be introduced to more constructive and creative things and make this knowledge progressive. This also provides the kids that kind of experience that they start to grab any knowledgeable thing very fast. Today no student is there who doesn’t know about online education because today students know the value of online learning and today students are doing very well with the help of online learning tools like institute ERP and LMS portal. These two tools institute ERP and LMS portal make online learning very easy and safe for the students. But as far as young children are considered they need extra care in order to make them more educated and fuller of knowledge. Preschool is a place which is these days considered as the best where these young children learn more than anywhere. Education in this tender age provides many of the good manners in the kids which usually kids don’t get after getting grown up. So, let’s understand the benefits of early childhood education.

The tutors of preschool and staff members along with management are very professionals because without being trained no one can run preschools and that is the rule therefore parents can be relaxed that their kids are in safe hands. These professionals have proper training, certificates and authority to deal with little kids. They are well trained people who understand the needs of the kids of preschool and also professionally well learned to collaborate with parents also in order to understand the needs of kids. In early childhood education kids get to know the feeling of belongingness along with their peers, tutors and those adults who care for them in preschool. There under supervision of caring and trained adults’ kids learn to socialise with people other than their parents and guardians. Apart from this they become good enough in social skills and interpersonal interactions too. such kids come out of their fear and become courageous to face anybody and any situation, moreover hesitation never becomes a hurdle in their way. Children are very soft hearted and sensitive too in their early years and this softness makes them blank slate therefore it should be taken care of that only good things should be written on these blank slates. For these their emotional, social and personal needs should be taken care of properly. Preschool tutors should notice their dilemmas and their struggles so that they can help them as much as they can. Preschool tutors should meet and discuss the progress of children with parents also so that something more progressive can be found out for the kids to be added to their education. This careful preschool makes a strong foundation to the base of education and intelligence level of the kids for further classes.

Also Read:  Who prepares the UPSC Syllabus? Is the Syllabus Changed for UPSC Exam 2022?

In the early years of education kids get proper time-period of attention under which they grow physically and psychologically. Usually, this level of attention is not available in the institutions for the grown-up kids but in preschools kids are attended very well. Due to this level of care kids also learn to be attentive and take care of their surroundings. Preschools are those great places for the kids which provide opportunities to the kids to quench their thirst for learning and kids are supported so much there that their curiosity for learning turns into passion and as they grow and get promoted to the higher classes, they begin to perform better than other classmates much better. Their social skills become so prominent that they can handle the outside world better as a kid and they can take care of themselves also. Preschools not only work on the growth of the kids in their early years but also they are proved to be the biggest support for the working parents.

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Who prepares the UPSC Syllabus? Is the Syllabus Changed for UPSC Exam 2022?



Who prepares the UPSC Syllabus? Is the Syllabus Changed for UPSC Exam 2022?

The Union Public Services Commission sets the UPSC syllabus and conducts Union Public Service examinations. The exam is administered in three parts.

  1. Preliminary Stage with the General Studies -1 and Civil Services Aptitude Test (CSAT) exam. 
  2. The Main Stage is the subjective part of the UPSC exam. There are 9 theory papers, including 4 General Studies papers, 2 Optional papers, 2 language papers and one essay paper. Language papers are of qualifying nature. A list of 48 subjects is given out of which you have to choose one optional subject. Any official language of India can be used to write the UPSC exam.  
  3. Interview Stage, which consists of the candidate’s personal interview.

The exam syllabus spans everything from local language papers, Science, Social Studies, General Knowledge, Engineering, Accountancy and Commerce, Agriculture and Veterinary Science, All streams of Science – Biology, Physics and Chemistry, Economics, Geography, History, Management, Law, Philosophy, International Relations and Civics, Public Administration, Statistics etc. 

Thorough syllabus preparation is required to achieve successful results in the UPSC exams. 

 UPSC Examination Syllabus:

UPSC Syllabus is different for different papers and is classified as follows. UPSC Exam 2022 syllabus has not changed. It has remained unchanged since a number of years.

  • GS 1 Paper covers History, geography, and Indian Society.
  • GS 2 paper covers Indian Polity, Constitution, Governance and International Relations
  • GS 3 paper has Indian Economy, Science and Technology, Agriculture and Environment as the chief focus.
  • GS 4 has Ethics, Integrity and Aptitude.

Preparation for UPSC IAS Exam

A thorough reading of all the NCERT materials is necessary apart from accessing past question paper banks, and repeated readings are required for preparing for UPSC exams.

Many online websites, such as BYJU’S Exam Prep, provide tips and material to facilitate your preparation for the examinations. Past question papers help you prepare for the UPSC exam, and they indicate the style and pattern of questioning, so you know the kind of questions you would be expected to answer in the exam. It will also help you review your preparation and analyse the quality of your preparation. 

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How can you download the syllabus for UPSC exams?

Many online websites like BYJU’S Exam Prep provide the syllabus, which can be downloaded easily in a PDF file. 

Apart from the latest syllabus, they also provide a bank of previous UPSC exam question papers, various tips to prepare for the exam, mock question papers, lessons, and other helpful aids. You can also directly read the syllabus on their website. 

BJYU’s Exam Prep also provides a helpful analysis of the trend of the pattern of questions asked in the previous UPSC exams.

This enables you to determine the subjects in an accumulation of questions and prepare for the exam accordingly. This analysis of previous question papers gives you a better understanding of the subjects from which they are drawn and the volume of questions in each subject. This is of great help in your UPSC examination preparation.

Is the syllabus for UPSC Exam 2022 changed?

The syllabus for UPSC Exam 2022 has not been changed and remains the same as the previous years’ UPSC Exams for 2021, 2020 and so on. 

You can very easily access the syllabus for UPSC Exam 2022 from BYJU’S Exam Prep website online. The syllabus for the UPSC Exams is extensive and detailed. It would help if you put in a lot of hard work, preparation and planning to cover all the topics in the syllabus at least 3 to 4 times before the exam. 

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Reasons to choose the SPOTO PMP dumps




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Why do you need PMP brain dumps?

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SPOTO assumes its strong part in working with you in venturing forward. For hopping on the stepping stool of the open door, they give you support by offering you a genuine condition of workmanship. You don’t have to look through the assessment content in the books since they give checked, tried and genuine inquiry and replies, planned by the eminent IT specialists. With the assistance of the, our job is to furnish you famous help with ensured progress in the assessment.


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SPOTO offers you chance of accomplishment with unconditional promise. We guarantee you that this valid material is the way to tackle the test questions without any problem. We give total acquaintance related with genuine test situation. It is useful for offering a strong help to breeze through the test in great score.

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