Get free NCERT solutions for class 6 Maths chapter 4:Basic Geometrical Ideas. Here you will find the latest updated solutions to prepare for the current academic session 2019-2020.Our experts have prepared easy and accurate solutions for all exercises given in **class 6 Maths NCERT chapter 4**. Students may read and download the solutions to refer the same whenever required.

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

(a) Five points

(b) A line

(c) Four rays

(d) Five line segments

**Solution.**

(a) Five points: D, E, O, B, C

(b) Name of a line:

(c) Four rays:

(d) Five line segments are:

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

**Solution.**

All the possible names for the given line can be written as follows:

**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.**

**4. How many lines can pass through**

**(a) one given point?**

**(b) two given points?**

**Solution.**

(a) Infinite number of lines can pass through a given point.

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

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

**Solution.**

**6. Consider the following figure of line MN. Say whether following statements are true or false in 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

**1. Classify the following curves as (i) open or (ii) closed.**

**Solution.**

(a) Open

(b) Closed

(c) Open

(d) Closed

(e) Closed

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

(a) Open curve

(b) Closed curve

**Solution.**

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

**Solution.**

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

(a) Is it a curve?

(b) Is it closed?

**Solution.**

(a) Yes, it is a curve.

(b) Yes, it is closed.

**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) Circle is a closed curve but not a polygon.

(b) Below is given an open curve made up entirely of line segments:

(c) It is not possible to have a polygon with two sides.

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

**Solution.**

Angles given in figure are:

∠DAB,∠ABC,∠BCD,∠CDA

**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) A is the point lying in the interior ∠DOE.

(b) C is the point lying in the exterior ∠EOF.

(c) B is the point lying on ∠EOF.

**3.Draw rough diagrams of two angles such that they have**

(а) 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.**

(a) In the following figure, O is the common point of ∠AOC and ∠BOD.

(b) In the following figure, O and Bare the common points in ∠AOB and ∠BOC.

(c) In the following figure, O, D and B are the common points in ∠AOB and ∠BOC.

(d) In the following figure, O, D, E and B are the common points in ∠AOB and ∠BOC.

(e) In the following figure, ray OB is common in both∠AOB and ∠DOB.

**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.**

Required triangle ABC is the given below:

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

**2.(a) Identify three triangles in the figure.**

**(6) Write the names of seven angles.**

**(c) Write the names of six line segments.**

**(d) Which two triangles have ****∠****B as common?**

**Solution.**

(a) Three triangles are:

∆ABC, ∆ABD and ∆ADC.

(b) Names of seven angles are:

∠ABC,∠ADB,∠BAD,∠ADC, ∠ACD,∠DAC,∠BAC

(c) Names of six line segments are:

(c) ∆ABC and ∆ABD have ∠B as common.

**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.**

Required quadrilateral PQRS is drawn as below:

Here PR and QS are its two diagonals.

The meeting point of the diagonals is O which lies 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.**

**Solution.**

Required quadrilateral KLMN is drawn as below:

(a) Two pairs of opposite sides are:

(KL, MN) and (NK, ML)

(b)Two pairs of opposite angles are:

∠LKN and ∠LMN, ∠KLM and ∠KNM

(c) Two pairs of adjacent sides are:

KL and KN, NM and ML

(d) Two pairs of adjacent angles are:

∠LKN and ∠KLM, ∠LMN, and ∠KNM

**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.**

(a) Centre of the circle is O.

(b) Three radii of the given circle are: OA, OB and OC.

(c) Diameter of the circle is AC.

(d) Chord of the circle is ED.

(e) Two points in the interior of the circle are O and P.

(f) Point in the exterior of the circle is Q.

(g) Sector of the circle is AOB (shaded region).

(h) Segment of the circle is ED (shaded region).

**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 its longest chord.

(b) No, every chord of a circle is not its 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.**

**Solution.**

Required circler can be drawn as follows:

In this circle,

(a) O is the center.

(b) OA is a radius.

(c) AB is a diameter.

(d) OBC is a sector (shaded region)

(e) ED in the segment(shaded region)

(f) P is in the interior of the circle.

(g) Q is in the exterior of the circle.

(h) BC is an arc of the circle.

**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; Two diameters of a circle always intersect at the centre of that circle.

(b) True

**Check chapter-wise NCERT Solutions for Class 6 Maths from the links given below:**

**NCERT Solutions for Class 6 Maths Chapter 1 - Knowing Our Numbers**

**NCERT Solutions for Class 6 Maths Chapter 2 - Whole Numbers**

**NCERT Solutions for Class 6 Maths Chapter 3 –Playing with Numbers**

NCERT solutions for other chapters will be provided here very soon. Check here for the detailed and appropriate solutions.