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## NCERT Solutions for Class 6 Maths Chapter 4: Basic Geometrical Ideas Ex 4.1

**Question 1:**

**Use the figure to name:**

**(a) Five points**

**(b) A line**

**(c) Four rays**

**(d) Five line segments**

**Solution**:

**Question 2:**

**Name the line given in all possible (twelve) ways, choosing only two letters**

**at a time from the four given.**

**Solution**:

The names are as followed

**Question 3:**

**Use the figure to name:**

**(a) Line containing point E.**

**(b) Line passing through A.**

**(c) Line on which O lies.**

**(d) Two pairs of intersecting lines.**

**Solution:**

**Question 4:**

**How many lines can pass though?**

**(a) one given point**

**(b) two given points**

**Solution**:

The answer to the following questions is,

(a) Infinite number of lines

(b) Only one line.

**Solution**:

The figure for the following questions is as follows;

**Question 6:**

**Consider the following figure of line MN . Say whether following statements**

**are true or false in the context of the given figure:**

**Solution**:

(a) True

(b) True

(c) True

(d) False

(e) False

(f) False

(g) True

(h) False

(i) False

(j) False

(k) True

## NCERT Solutions for Class 6 Maths Chapter 4: Basic Geometrical Ideas Ex 4.2

**Question 1:**

**Classify the following curves as (i) Open or (ii) Closed.**

**Solution**:

They are classified in the following way,

(a) – Open

(b) – Closed

(c) – Open

(d) – Closed

(e) – Closed

**Question 2:**

**Draw rough diagrams to illustrate the following:**

**(a) Open curve**

**(b) Closed curve**

**Solution**:

The following are the examples of the following,

(a) Open Curve.

(b) Closed Curve.

**Question 3:**

**Draw any polygon and shade its interior.**

**Solution**

:

**Question 4:**

**Consider the given figure and answer the questions:**

**(a) Is it a curve?**

**(b) Is it closed?**

**Solution**:

From the given figure,

(a) Yes, it is a curve.

(b) Yes, it is closed.

**Question 5:**

**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**:

(a)

(b)

(c) Polygon, not possible.

## NCERT Solutions for Class 6 Maths Chapter 4: Basic Geometrical Ideas Ex 4.3

**Question 1:**

**Name the angles in the given figure:**

**Solution**:

**Question 2:**

**In the given diagram, name the point(s):**

**(a) In the interior of DOE.**

**(b) In the exterior of EOF.**

**(c) On EOF.**

**Solution**:

(a) Point interior of DOE: A

(b) Points exterior of EOF: C, A, D

(c) Points on EOF: E, O, B, F

**Question 3:**

**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**:

The diagram for each question is as follows,

(a)

Here, angle AOB and BOC have 1 common point O.

(b)

Here, angles AOB and BOP have 2 common points as O and B.

(c)

Here, angles EOA and AOB have 4 common points as O, D, C, and A.

(e)

Here, ray OA is common.

## NCERT Solutions for Class 6 Maths Chapter 4: Basic Geometrical Ideas Ex 4.4

**Question 1:**

**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:Question 1:**

**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**:

A is one of the vertex of the triangle and it’s neither in the exterior nor in the interior.

**Question 2:**

**(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**:

## NCERT Solutions for Class 6 Maths Chapter 4: Basic Geometrical Ideas Ex 4.5

**Question 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**:

The name of the diagonals is SQ and PR.

The meeting point of the diagonals is inside the quadrilateral.

**Question 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**:

**Question 3:**

**Investigate:**

**Use strip and fasteners to make a triangle and a quadrilateral.**

**Try to push inward at any one vertex of the triangle. Do the same to the**

**quadrilateral. Is the triangle distorted? Is the quadrilateral distorted? Is**

**the triangle rigid? Why is it that structures like electric towers make use of**

**triangular shapes and not quadrilateral?**

**Solution**:

O is common to both the angles AOC and BOC.

No, the triangle is not distorted. Quadrilateral is distorted and also the triangle is rigid.

Electric towers make use of triangular shape.

## NCERT Solutions for Class 6 Maths Chapter 4: Basic Geometrical Ideas Ex 4.6

**Question 1:**

**From the figure, identify:**

(a) The centre of circle.

(b) Three radii.

(c) A diameter.

(d) A chord.

(e) Two points in the interior.

(f) A point in the exterior.

(g) A sector.

(h) A segment

**Solution**:

From the figure,

(a) Centre is O

(b) Radii: OA, OB and OC

(c) A diameter: AC

(d) A chord: ED

(e) Interior points: O, P

(f) Exterior points: Q

(g) A sector: OAB

(h) A segment: ED

**Question 2:**

**(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.

**Question 3:**

**Draw any circle and mark:**

**(a) Its centre.**

**(b) A radius.**

**(c) A diameter.**

**(d) A sector.**

**Solution**: According to the question the diagram is as follows,

Here, point O is the centre, AO is the radius, AB is the diameter, and AOC is a sector.

**Question 4:**

**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