**Class 6 Maths Chapter 4 Basic Geometrical Ideas**

**NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas, ****(Maths) exam are Students are taught thru NCERT books in some of state board and CBSE Schools. As the chapter involves an end, there is an exercise provided to assist students prepare for evaluation. Students need to clear up those exercises very well because the questions withinside the very last asked from those.**

**Sometimes, students get stuck withinside the exercises and are not able to clear up all of the questions. To assist students, solve all of the questions and maintain their studies without a doubt, we have provided step by step NCERT Solutions for the students for all classes. These answers will similarly help students in scoring better marks with the assist of properly illustrated solutions as a way to similarly assist the students and answering the questions right.**

**NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas**

**Class 6 Maths Chapter 4 Basic Geometrical Ideas**

**Exercise 4.1**

page no: 74

**1. Use the figure to name:**

(a) Five points

(b) A line

(c) Four rays

(d) Five line segments

Solutions:

**(a)The five points are D, E, O, B and C**

**2. Name the line given in all possible (twelve) ways, choosing only two letters at a time from the four given.**

**Solutions:**

**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.

Solutions:

**4. How many lines can pass through (a) one given point? (b) two given points?**

Solutions:

(a) Countless lines can pass through a given point.

(b) Only one line can pass through a two given points.

**5. Draw a rough figure and label suitably in each of the following cases:**

**(c) Line l contains E and F but not D.**

Solutions:

(a)

(b)

**(c)**

(d)

Solutions:

(a)True

(b) True

(c) True

(d) False

(e) False

(f) False

(g) True

(h) False

(i) False

(j) False

(k) True

**Exercise 4.2**

PAGE NO: 78

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

Solutions:

(a)The given curve is an open curve

(b) The given curve is closed curve

(c) The given curve is open curve

(d) The given curve is closed curve

(e) The given curve is closed curve

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

(a) Open curve

(b) Closed curve

Solutions

(a) The below figure is the open curve

(b)The below figure is the closed curve

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

Solutions:

The below figure is the polygon with interior shade

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

(a) Is it a curve?

(b) Is it closed?

Solutions:

(a)Yes, it is a curve

(b) Yes, it is closed curve

**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.

Solutions:

(a) The below figure is the closed figure but not a polygon

(b)The below figure is an open curve made up entirely of line segments

(c) No its not possible, as the polygon having least number of sides is a triangle which has three sides.

**Exercise 4.3**

page no: 80

**1. Name the angles in the given figure.**

Solutions:

The angles are ∠DAB, ∠ABC, ∠BCD and ∠CDA

**2. In the given diagram, name the points(s)**

(a) In the interior of ∠DOE

(b) In the exterior of ∠EOF

(c) On ∠EOF

Solutions:

(a)The point in the interior of ∠DOE is A

(b) The point in the exterior of ∠EOF is C, A and D

(c) The points on ∠EOF are E, B, O and F

**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

Solutions:

(a) O is common point between ∠COD and ∠AOB

(b) O and B are common points between ∠AOB and ∠BOC

(c) O, E and B are common points between ∠AOB and ∠BOC

(d) O, E, D and A are common points between ∠BOA and ∠COA

(e) OC is common ray between ∠BOC and ∠AOC

**Exercise 4.4**

page no: 81

**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?**

Solutions:

Point A lies on the given triangle ABC. It lies neither in interior nor exterior.

**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?

Solutions:

(a)The three triangles are ∠ABD, ∠ACB, ∠ADC

(b) The angles are ∠BAC, ∠BAD, ∠CAD, ∠ADB, ∠ADC, ∠ABC, ∠ACB

(d) ∠ABD and ∠ABC are triangles which have ∠B as common.

**Exercise 4.5**

Page no: 82

**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?**

Solutions:

PR and QS are the diagonals**. **They meet at point O which is in the interior of the quadrilateral.

**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.

Solutions:

(d) Two pairs of adjacent angles are ∠K, ∠L and ∠M, ∠N or ∠K, ∠L and ∠L, ∠M

**Exercise 4.6**

page no: 84

**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

Solutions:

**(a) The centre of circle is O**

**(e) Two points in the interior are O and P**

**(f) A point in the exterior is Q**

**(g) A sector is AOB i.e shaded region**

**(h) A segment is ED i.e shaded region**

**2. **(a) Is every diameter of a circle also a chord?

(b) Is every chord of a circle also a diameter?

Solutions:

(a)Yes every diameter of a circle is also a chord. Diameter is also called as longest chord.

(b) No, every chord is not a diameter.

**3. 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

Solutions:

**(a)The centre of the circle is O.**

**(b) The radius is OC**

**(d) A sector is AOC**

**(e) A segment is DE**

**(f) A point in its interior is O**

**(g) A point in its exterior is F**

**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.

Solutions:

(a)True, two diameters will always intersect each other at the centre of the circle.

(b) True, the centre of the circle will always be in its interior.