Find the best tutors and institutes for Class 9 Tuition
Learn Definitions, axioms and postulates
Welcome to CBSE Class 9 Mathematics! In the chapter "Introduction to Euclid’s Geometry," we take a fascinating journey back in time to understand how modern geometry was built. Before mathematicians can prove complex theorems, they need a solid foundation of undeniable truths. The ancient Greek mathematician Euclid provided this framework by laying down basic ground rules in his famous work, 'Elements'. He started with simple definitions to describe basic shapes and concepts, and then established foundational truths known as axioms and postulates. Understanding these distinct concepts is essential because they form the very building blocks of every geometric proof you will encounter in high school.
Let's break down these three fundamental pillars. First, Definitions are basic descriptions of geometric entities, such as Euclid's statement that "a point is that which has no part" or "a line is breadthless length." While we now consider terms like point and line to be undefined to avoid circular logic, Euclid's definitions give us a conceptual starting point. Next, we have Axioms (often called common notions). These are self-evident truths that are assumed to be true across all branches of mathematics. For example, the axiom stating "Things which are equal to the same thing are equal to one another" applies equally to algebra, arithmetic, and geometry. Finally, Postulates are also assumed universally true, but they are strictly related to geometry. A famous example is Euclid's First Postulate: "A straight line may be drawn from any one point to any other point." Together, axioms and postulates act as unprovable but obvious starting points used to logically deduce complex mathematical truths.
The diagram above clearly distinguishes the three key concepts laid out by Euclid. In the blue section, you can see Definitions, where simple concepts like a "point" or a "line" are given formal mathematical meaning. The green section illustrates an Axiom. Notice how the logical reasoning "If a=b and b=c, then a=c" does not rely on geometric shapes; it is a universal mathematical truth. On the right, the red section highlights a Postulate. It shows two distinct points connected by a straight line, visually representing Euclid's First Postulate, which is an assumption specific only to geometry. In your CBSE Class 9 exams, you will frequently be asked to differentiate between axioms and postulates, or to apply these exact statements as reasons to justify the steps in your geometric proofs.
Mastering Euclid’s definitions, axioms, and postulates is just the beginning of your journey into higher-level geometry. If you find differentiating between these concepts challenging or need help applying them to complex theorem proofs, expert guidance can make a world of difference. On UrbanPro, you can easily connect with highly experienced, verified CBSE Class 9 Mathematics tutors. Whether you prefer personalized online tutoring from the comfort of your home or local offline tuition, UrbanPro provides the perfect platform to find the right tutor who can help you build a strong geometric foundation and ace your upcoming math exams.
Other Concepts in Introduction to Euclid’s Geometry
Other Concept Videos for Definitions, axioms and postulates
Geometry Basics: Definitions, Axioms, and Postulates
CBSE - Class 9>Mathematics>Introduction to Euclid’s Geometry>Definitions, axioms and postulates
Geometry Basics: Definitions, Axioms, and Postulates
CBSE - Class 9>Mathematics>Introduction to Euclid’s Geometry>Definitions, axioms and postulates
Top Tutors who teach Definitions, axioms and postulates
Teaching since last 20 years
Amit ji is a fantastic teacher. My daughter is very happy with her studies. He is exactly what she needed, a teacher with deep understanding of his subject and a very good communicator. If there is one gripe that I may mention, it's time. We would love to have more classes to cover Physics, but he is completely booked for his time. I would highly recommend him. Thank you.
I gained extensive experience in delivering high-quality education following the CBSE/ICSE curriculum. My key responsibilities included: Classroom Teaching: Effectively taught Mathematics, Physics and Chemistry to students of classes IX, ensuring alignment with the CBSE/ ICSE syllabus and fostering a deep understanding of key concepts. Curriculum Planning: Designed and implemented lesson plans that adhered to the CBSE guidelines, ensuring comprehensive coverage of topics while keeping in mind the varying learning needs of students. Student Assessment: Created and administered tests, quizzes, and assignments in accordance with the CBSE exam pattern. Monitored student performance and provided constructive feedback to facilitate continuous improvement. Interactive Learning: Encouraged an interactive classroom environment, integrating various teaching aids such as multimedia presentations, hands-on activities, and group discussions to enhance student engagement and understanding. Preparation for Board Exams: Provided focused support for students appearing for their CBSE/ICSE board exams by conducting regular revision sessions, mock tests, and personalized guidance to help them excel. Parental Communication: Maintained regular communication with parents regarding student progress, attendance, and overall development. Organized parent-teacher meetings to ensure a collaborative approach to student growth. Co-curricular Involvement: Actively participated in school events, projects, and extracurricular activities, fostering holistic development among students. Professional Development: Engaged in continuous professional development through workshops and CBSE training programs to stay updated with the latest educational practices and policies.
I teach Math and Science to 8th-12th standard students and have been teaching for more than 10 years. Batch of 2 Students: I conduct these small batches with a pair of students of the same class and the education board (I cover all popular boards CBSE, ICSE, IGCSE etc.). Works for those students/parents who are looking for individual attention for their kids but still want it to be a little affordable. *3 classes per week (So 12 a month) *Maths and Science (Also English Grammar and Literature) *Fee Rs. 4500/- per month/12 classes. Batch of 6 Students: I conduct these small batches with 5-6 students of the same class and the education board (I cover all popular boards CBSE, ICSE, IGCSE etc.). *4 classes per week (So 16 a month) *Maths and Science *Fee Rs. 4000/- per month/16 classes. I will start the classes immediately once the first kid enrolls. ------------------------------------------------------------------------------- Individual/Private/One-to-One classes: I conduct these one to one classes for those students willing to have one to one setup (I cover all popular boards CBSE, ICSE, IGCSE etc.). *3 classes per week (So 12 a month) *Maths and Science (Also English Grammar and Literature) *Fee Rs. 7000/- per month/12 classes. ------------------------------------------------------------------------------- I took classes and batches in different institutions.
The teacher is very good. He understands the students strength and weakness and decides the pace of learning. He also tries to make the student comfortable and at ease with his/her capacity and then works on the child. It is not just Math he works on but the child's confidence and comfort with the subject. Highly recommended.
As a passionate mathematics teacher, I have always enjoyed imparting knowledge to others. I am a B.Tech graduate in Electronics and Communication. I have been teaching mathematics for over four years, and my love for the subject has grown stronger with time. I started teaching as a part-time tutor while pursuing my engineering degree and fell in love with the profession. After completing my degree, I worked with Byjus, one of the leading Edtech companies in India, as a mathematics teacher for two years. While I enjoyed my time at Byju's, I could do more as a teacher and wanted to explore new avenues. I joined Vedantu, an online learning platform, where I have been teaching mathematics for the last two years. I started my journey as a math teacher out of pure passion. Mathematics has always been my favourite subject, and I enjoyed solving problems and equations from a young age. As I grew older, I realised I had a natural talent for teaching, and I decided to pursue it as a career. Currently, I provide mathematics classes for students from sixth to twelfth for all boards, including ICSE, CBSE, and West Bengal. I teach offline and online classes, each lasting for one and a half hours. I use interactive tools such as Zoom, Pentab, and One Note to make my lessons engaging and interactive for my students. To help my students excel in mathematics, I provide them with reference books, notes, and in-built assignments to test their knowledge. I also conduct monthly tests to assess their progress and identify improvement areas. Teaching on UrbanPro has allowed me to interact with students from different parts of the country and help them realise their full potential in mathematics. I want to continue making a positive impact in the lives of my students and help them develop a love for mathematics, just like I did
Avishake Sir is an exceptional maths teacher! Engaging, patient, and effective. He break down complex concepts into easy-to-understand bits , provide individual attention and boost confidence. Highly recommended!"
I am a teacher and I have been teaching for the past 20 years. l am presently teaching in a school. l have done MSc in Maths and have taught many students.
Thanks Ma'am for supporting Anvi in the subject. She has been getting more comfortable and relaxed with the theory and concepts in mathematics. Her fear is waning away and she shows an increased interest in the subject. I will definitely recommend you to all prospective parents. Thanks again!
Find more Tutor for Definitions, axioms and postulates in your City
- Delhi Mathematics Tutors
- Bangalore Mathematics Tutors
- Hyderabad Mathematics Tutors
- Mumbai Mathematics Tutors
- Chennai Mathematics Tutors
- Kolkata Mathematics Tutors
- Gurgaon Mathematics Tutors
- Pune Mathematics Tutors
- Noida Mathematics Tutors
- Ghaziabad Mathematics Tutors
- Lucknow Mathematics Tutors
- Jaipur Mathematics Tutors
FAQ
What is the meaning of Definitions axioms and postulates?
It refers to a specific mathematical method or property in Introduction to Euclid’s Geometry used to solve problems involving Definitions axioms and postulates.
Why is Definitions axioms and postulates important for CBSE - Class 9 exams?
This concept is crucial for the exams as questions related to Introduction to Euclid’s Geometry and specifically Definitions axioms and postulates are very common. It helps secure marks in the section effectively.
Is Definitions axioms and postulates part of the latest NCERT syllabus?
Yes, Definitions axioms and postulates is an integral part of the CBSE - Class 9 NCERT Mathematics syllabus. It is a key topic covered in the Introduction to Euclid’s Geometry chapter.
What are common mistakes students make with Definitions axioms and postulates?
Students often miss the minute details or fundamental definitions of Definitions axioms and postulates. Regular revision and practice are needed to master the nuances.
How should I approach learning Definitions axioms and postulates?
Start by understanding the formulas and logic, then practice applying them to simple problems. Solve the examples given in the NCERT textbook before moving to exercise problems.
How can UrbanPro help me understand Definitions axioms and postulates better?
UrbanPro connects you with experienced Mathematics tutors who can explain Definitions axioms and postulates with simple examples. You also get access to doubt-clearing sessions and mock tests for better preparation.