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Learn Bisecting angles and line segments

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How to Bisect Angles and Segments

Welcome to your CBSE Class 9 Mathematics journey! In the "Constructions" chapter, one of the most foundational skills you will learn is bisecting. Bisection simply means dividing a geometric figure into two exactly equal halves. Whether you are dealing with a straight path (a line segment) or a corner (an angle), knowing how to accurately split them down the middle is mathematically crucial. This fundamental concept acts as a building block for drawing complex shapes like triangles, locating incenters and circumcenters, and constructing specific angles like 45° or 30° without ever using a protractor.

To bisect these figures, we rely entirely on the precise use of a compass and a straightedge (ruler). For a line segment bisector (also called a perpendicular bisector), the logic is based on creating intersecting arcs from both endpoints of the line (let's say A and B). You must open your compass to a radius strictly greater than half the length of the line segment. Striking arcs above and below the line from both A and B creates two exact intersection points; joining them cuts the line perfectly in half at exactly 90°. For an angle bisector, the goal is to split the opening angle equally. We first draw a reference arc from the angle's vertex to cut both arms. Using those two newly created intersection points as centers, we draw two more intersecting arcs outwards. The line drawn from the vertex straight through this final intersection point is your precise angle bisector.

Bisecting Line Segments and Angles 1. Perpendicular Bisector A B P Q 90° Compass radius > 1/2 AB 2. Angle Bisector O E F P 30° 30° Intersecting arcs from E & F

Observe the diagram above, which visually separates these two primary constructions. On the left, you can see the step-by-step logic of the Perpendicular Bisector of line segment AB. The dashed red line accurately divides AB into two perfectly equal parts at a 90-degree angle, simply formed by connecting the top and bottom arc intersections (marked as points P and Q). On the right, the diagram maps out the Angle Bisector. Starting from vertex O, an initial green arc is drawn to cut the angle's arms at points E and F. By safely placing the compass needle at E and then at F (without changing the radius width), two outer arcs are drawn to intersect at point P. Drawing the red dashed line from O exactly through P splits the original 60° angle into two distinct, equal 30° angles. In your school exams, retaining these faint compass construction marks is highly essential, as examiners specifically look for these intersection points to verify your geometrical process.

Mastering compass and straightedge constructions requires patience, steady hands, and consistent practice. If you find yourself struggling to visualize exactly where to place your compass point or how to creatively combine these methods to construct complex angles like 75° or 135°, expertly guided practice can make a huge difference. On UrbanPro, you can easily connect with highly experienced, verified CBSE Class 9 Mathematics tutors who specialize in making geometry simple and highly scoring. Whether you prefer personalized one-on-one online tuition or engaging local offline classes, UrbanPro offers the perfect tutor to help you successfully ace your exams and build total confidence in Mathematics.


Other Concepts in Constructions


Other Concept Videos for Bisecting angles and line segments

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How to Bisect Angles and Segments

CBSE - Class 9>Mathematics>Constructions>Bisecting angles and line segments


How to Bisect Angles and Segments video thumbnail

How to Bisect Angles and Segments

CBSE - Class 9>Mathematics>Constructions>Bisecting angles and line segments

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Top Tutors who teach Bisecting angles and line segments

(68)
superTutorSuper Tutor
locationImg Sector 92, Gurgaon
20 yrs of Exp 20 students
greenClock 1277 hrs of classes completed
rsIcon 800 per hour
Teaching mathematics since last 20 years. Doing research on Vedic mathematics
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Teaching since last 20 years

Nandini Mishra

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.

Skills: Mathematics , Physics and more
Also teaches: Class 12 Tuition, BSc Tuition and more

Sai V. Class 9 Tuition trainer in Madappanahalli
(138)
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locationImg Itagalpura Main Rd, Madappanahalli
17 yrs of Exp 43 students
greenClock 3515 hrs of classes completed
rsIcon 400 per hour
MSc, BEd , (Phd), Member of Royal Society UK
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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.

Skills: Mathematics , Physics and more

(59)
superTutorSuper Tutor
locationImg Sector 5, Dwarka, Delhi
10 yrs of Exp 32 students
greenClock 1150 hrs of classes completed
rsIcon 500 per hour
10 Yrs in Teaching, Conduct Batch Of Two Kids, One-to-One classes. ShortTermPrep & LongTermClasses.
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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.

Surabhi rai

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.

Skills: Mathematics , Physics and more
Also teaches: Python Training, Spoken English and more

Avishake Chatterjee Class 9 Tuition trainer in Kolkata
(62)
superTutorSuper Tutor
locationImg Behala, Kolkata
8 yrs of Exp 7 students
greenClock 947 hrs of classes completed
rsIcon 700 per hour
MATHS EXPERT having an experience of 6+years
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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

Aaa Mukherjee

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!"

Skills: Mathematics
Also teaches: Class I-V Tuition, Class 11 Tuition and more

(25)
superTutorSuper Tutor
locationImg Rohini Sector-24, Delhi
20 yrs of Exp 10 students
greenClock 1397 hrs of classes completed
rsIcon 450 per hour
Experienced Maths teacher with more than 20 years of experience.
Online Classes Online Classes

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.

Amit Kumar

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!

Skills: Mathematics , Physics and more
Also teaches: Class 8 Tuition, Class 7 Tuition and more

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Other Subjects in CBSE - Class 9


FAQ

What is the meaning of Bisecting angles and line segments?

It refers to a specific mathematical method or property in Constructions used to solve problems involving Bisecting angles and line segments.

Why is Bisecting angles and line segments important for CBSE - Class 9 exams?

This concept is crucial for the exams as questions related to Constructions and specifically Bisecting angles and line segments are very common. It helps secure marks in the section effectively.

Is Bisecting angles and line segments part of the latest NCERT syllabus?

Yes, Bisecting angles and line segments is an integral part of the CBSE - Class 9 NCERT Mathematics syllabus. It is a key topic covered in the Constructions chapter.

What are common mistakes students make with Bisecting angles and line segments?

Students often miss the minute details or fundamental definitions of Bisecting angles and line segments. Regular revision and practice are needed to master the nuances.

How should I approach learning Bisecting angles and line segments?

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 Bisecting angles and line segments better?

UrbanPro connects you with experienced Mathematics tutors who can explain Bisecting angles and line segments with simple examples. You also get access to doubt-clearing sessions and mock tests for better preparation.

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