NCERT Solutions for Class 6 – Complete Chapter-wise Study Material
4. Basic Geometrical Ideas is one of the most important chapters in the Class 6 Mathematics English NCERT Solutions curriculum. This chapter plays a significant role in helping students build a strong conceptual foundation while preparing for school examinations, class tests, unit tests, half-yearly examinations, annual examinations, and CBSE board assessments. The chapter has been carefully designed according to the latest NCERT syllabus, making it an essential part of every student's study plan.
The 4. Basic Geometrical Ideas - Class 6 Mathematics English NCERT Solutions available on ATP Education explain every question in a simple, accurate, and step-by-step manner. Each answer is prepared according to the latest CBSE guidelines so that students can understand the concepts clearly without confusion. Whether you are completing your homework, revising before examinations, or strengthening your understanding of the subject, these solutions provide reliable academic support throughout your learning journey.
One of the biggest advantages of studying 4. Basic Geometrical Ideas is that it helps students understand important concepts, definitions, examples, and textbook exercises in an organized way. Instead of memorizing answers, students learn how to develop logical thinking, improve analytical skills, and write well-structured answers in examinations. This chapter also helps improve problem-solving ability and encourages conceptual learning, which is essential for scoring higher marks in school and competitive examinations.
Our Class 6 Mathematics NCERT Solutions cover all textbook questions, important exercise questions, and chapter-wise explanations in English Medium. Every solution is written in easy-to-understand language, allowing students to revise the chapter quickly before examinations. Regular practice of these solutions improves confidence, strengthens subject knowledge, and reduces examination stress.
Students preparing for school assessments should carefully study 4. Basic Geometrical Ideas because questions from this chapter are frequently asked in objective questions, short answer questions, long answer questions, competency-based questions, and case-study questions. Understanding the concepts explained in this chapter also helps students connect related topics from other chapters, making overall learning more effective and meaningful.
At ATP Education, we continuously update our Class 6 Mathematics English NCERT Solutions according to the latest NCERT textbooks and CBSE curriculum. Students can confidently use these chapter-wise solutions for daily study, homework assistance, quick revision, examination preparation, and self-learning. By studying 4. Basic Geometrical Ideas thoroughly and practising every question regularly, students can strengthen their concepts, improve writing skills, and achieve better academic performance in both school and board examinations.
4. Basic Geometrical Ideas - Class 6 Mathematics English NCERT Solutions
4. Basic Geometrical Ideas
Exercise 4.1
Exercise 4.1
Q1. Use the figure to name:
(a) Five points
Solution: The five point of this figure:- B, C, O, E, D
(b) A line
Solution: DB
(c) Four rays
Solution: OB, OC, OP, OD
(d) Five line segments
Q2. Name the line given in all possible (twelve) ways, choosing only two letters at a time from the four given.
Q3. Use the figure to name :
Q4. How many lines can pass through
(a) one given point?
Solution: Infinity lines can pass through one point.
(b) Two given points?
Solution: Only one lines can pass through one point.
Q5. Draw a rough figure and label suitably in each of the following cases:.
(a) Point P lies on AB.
Solution:
4. Basic Geometrical Ideas
Exercise 4.2
Exercise 4.2
Q1. Classify the following curves as (i) Open or (ii) Closed.
Solution:
(i) Open curves : (a) and (c)
(ii) Close curves : (b) (d) and (e)
Q2. Draw rough diagrams to illustrate the following :
(a) Open curve (b) Closed curve.
Solution:
Q3. Draw any polygon and shade its interior.
Solution:
Q4. Consider the given figure and answer the questions :
(a) Is it a curve? (b) Is it closed?
Solution:
(a) Is it a curve?
Solution: yes, it is a curve
(b) Is it closed?
Solution: yes, it is a closed
Q5. Illustrate, if possible, each one of the following with a rough diagram:
(a) A closed curve that is not a polygon.
(b) An open curve made up entirely of line segments.
(c) A polygon with two sides.
Solution:
(c) A polygon with two sides.
Solution: The polygon can be made with three or more sides. There is no polygon with two sides.
4. Basic Geometrical Ideas
Exercise 4.3
Exercise 4.3
Q1. Name the angles in the given figure.
Solution: Solution: ∠ADC , ∠DCB, ∠CBA and ∠BAD
Q2. In the given diagram, name the point(s)
(a) In the interior of ∠DOE
(b) In the exterior of ∠EOF
(c) On ∠EOF
(a) In the interior of ∠DOE
Solution: Point A
(b) In the exterior of ∠EOF.
Solution: Point C
(c) On ∠EOFSolution: Point B
Q3. Draw rough diagrams of two angles such that they have
(a) One point in common.
(b) Two points in common.
(c) Three points in common.
(d) Four points in common.
(e) One ray in common.
Solution:
4. Basic Geometrical Ideas
Exercise 4.4
Exercise 4.4
Q1. Draw a rough sketch of a triangle ABC. Mark a point P in its interior and a point Q in its exterior. Is the point A in its exterior or in its interior?
Solution:
Q2. (a) Identify three triangles in the figure.
(b) Write the names of seven angles.
(c) Write the names of six line segments.
(d) Which two triangles have ∠B as common?
Solution:
4. Basic Geometrical Ideas
Exercise 4.5
Exercise 4.5
1. Draw a rough sketch of a quadrilateral PQRS. Draw its diagonals. Name them. Is the meeting point of the diagonals in the interior or exterior of the quadrilateral?
Solution:
Diagonals of quadrilateral PQRS are PR and QS
Meeting Point is O which is interior of quadrilateral PQRS.
2. Draw a rough sketch of a quadrilateral KLMN. State,
(a) two pairs of opposite sides,
(b) two pairs of opposite angles,
(c) two pairs of adjacent sides,
(d) two pairs of adjacent angles.
Solution:
(a) two pairs of opposite sides,
Solution:
(i) KL and NM
(ii) KN and LM
(b) two pairs of opposite angles,
Solution:
(i) ∠K and ∠M
(ii) ∠L and ∠N
(c) two pairs of adjacent sides,
Solution:
(i) KN and KL
(ii) KL and ML
(d) two pairs of adjacent angles.
Solution:
(i) ∠K and ∠L
(ii) ∠M and ∠N
4. Basic Geometrical Ideas
Exercise 4.6
Exercise 4.6
Q1. From the figure, identify :
(a) the centre of circle
Solution: The centre of circle is O.
(b) three radii
Solution: Three radii are OA, OB and OC.
(c) a diameter
Solution: AC is diameter of circle.
(d) a chord
Solution: ED is a chord.
(e) two points in the interior
Solution: Two points in the interior are P and O.
(f) a point in the exterior
Solution: Q is the point in the exterior of circle.
(g) a sector
Solution: AOB forms sector.
(h) a segment
Solution: ED forms segment.
Q2. (a) Is every diameter of a circle also a chord?
(b) Is every chord of a circle also a diameter?
Solution:
(a) Yes, every diameter of a circle is also a chord.
(b) No, every chord of a circle is not a diameter.
Q3. Draw any circle and mark
(a) its centre
(b) a radius
(c) a diameter
(d) a sector
(e) a segment
(f) a point in its interior
(g) a point in its exterior
(h) an arc
Solution:
(a) its centre : O
(b) a radius : OA
(c) a diameter : AC
(d) a sector : AOB
(e) a segment : ED
(f) a point in its interior : Point P
(g) a point in its exterior : Point Q
(h) an arc : arch AB
Q4. Say true or false :
(a) Two diameters of a circle will necessarily intersect.
(b) The centre of a circle is always in its interior.
Solution:
(a) True
(b) True
Mathematics
Class 6 (English Medium)
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