# Basic geometrical ideas

**Class –VI**

**Mathematics**

**(Ex. 4.1)**

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

(a)Five points

(b)A line

(c)Four rays

(d)Five line segments

**Answer:**

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

(b) A line: DE¯¯¯¯¯¯¯,DE¯,DB¯¯¯¯¯¯¯,DB¯,OE¯¯¯¯¯¯¯,OE¯,OB¯¯¯¯¯¯¯OB¯

(c) Four rays: OD−→−,OD→,OE−→−,OE→,OC−→−,OC→,OB−→−OB→

(d) Four line segments: DE¯¯¯¯¯¯¯,DE¯,OE¯¯¯¯¯¯¯,OE¯,OC¯¯¯¯¯¯¯¯,OC¯,OB¯¯¯¯¯¯¯,OB¯,, OD¯¯¯¯¯¯¯¯OD¯

NCERT Solutions for Class 6 Maths Exercise 4.1

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

**Answer: **AB¯¯¯¯¯¯¯,AB¯,AC¯¯¯¯¯¯¯,AC¯,AD¯¯¯¯¯¯¯¯,AD¯,BC¯¯¯¯¯¯¯,BC¯,BD¯¯¯¯¯¯¯,BD¯,CD¯¯¯¯¯¯¯,CD¯,BA¯¯¯¯¯¯¯,BA¯,CA¯¯¯¯¯¯¯,CA¯,DA¯¯¯¯¯¯¯¯,DA¯,CB¯¯¯¯¯¯¯,CB¯,DB¯¯¯¯¯¯¯,DB¯,DC¯¯¯¯¯¯¯DC¯

**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.

**Answer: **(a) A line containing E = AE¯¯¯¯¯¯¯AE¯ or FE¯¯¯¯¯¯¯FE¯

(b) A line passing through A = AE¯¯¯¯¯¯¯AE¯ or DE¯¯¯¯¯¯¯DE¯

(c) A line on which O lies = CO¯¯¯¯¯¯¯¯CO¯ or OC¯¯¯¯¯¯¯¯OC¯

(d) Two pairs of intersecting lines are : AD¯¯¯¯¯¯¯¯,AD¯,CO¯¯¯¯¯¯¯¯CO¯ and AE¯¯¯¯¯¯¯AE¯, FE¯¯¯¯¯¯¯FE¯

NCERT Solutions for Class 6 Maths Exercise 4.1

**Question 4.**How many lines can pass though:

(a) one given point?

(b) two given points

**Answer:** (a) Infinite number of lines can pass through one given point.

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

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

(a)Point P lies on AB¯¯¯¯¯¯¯.AB¯.

(b) XY¯¯¯¯¯¯¯¯XY¯ and PQ¯¯¯¯¯¯¯PQ¯ intersect at M.

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

(d) OP¯¯¯¯¯¯¯OP¯ and OQ¯¯¯¯¯¯¯¯OQ¯ meet at O.

**Answer:** Sol.

NCERT Solutions for Class 6 Maths Exercise 4.1

**Question 6.**Consider the following figure of line MN¯¯¯¯¯¯¯¯MN¯. Say whether following statements are true or false in the context of the given figure:

(a)Q, M, O, N, P are points on the line MN¯¯¯¯¯¯¯¯MN¯.

(b)M, O, N are points on a line segment MN¯¯¯¯¯¯¯¯MN¯.

(c)M and N are end points of line segment MN¯¯¯¯¯¯¯¯MN¯.

(d)O and N are end points of line segment OP¯¯¯¯¯¯¯OP¯.

(e)M is one of the end points of line segment QO¯¯¯¯¯¯¯¯QO¯.

(f)M is point on ray OP−→−OP→.

(g)Ray OP−→−OP→ is different from ray OP−→−OP→.

(h)Ray OP−→−OP→same as ray OM−→−.OM→..

(i)Ray OM−→−.OM→. is not opposite to ray OP−→−OP→.

(j)O is not an initial point of NP¯¯¯¯¯¯¯NP¯ and NM¯¯¯¯¯¯¯¯NM¯.

**Answer:** (a) True, (b) True, (c) True, (d) False, (e) False, (f) False, (g) True, (h) False, (i) False, (j) False, (k) True

**(Ex. 4.2)**

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

**Answer:** (a) Open curve

(b) Closed curve

(c) Open curve

(d) Closed curve

(e) Closed curve

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

(a)Open curve

(b)Closed curve

**Answer:**Opencurves:

Closed curves

NCERT Solutions for Class 6 Maths Exercise 4.2

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

**Answer:** Polygon ABCDEF

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

(a)Is it a curve?

(b)Is it closed?

**Answer:** (a) Yes, it is a curve.

(b) Yes, it is closed.

NCERT Solutions for Class 6 Maths Exercise 4.2

**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.

**Answer:** (a)

(b)

(c) Polygon with two sides cannot be draw.

**(Ex. 4.3)**

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

**Answer:** There are four angles in given figure:

∠∠ABC, ∠∠CDA, ∠∠DAB, ∠∠DCB

**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.

**Answer:**

(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.

**Answer:**

(a)

(b)

(c)

(d)

(e)

**(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?

**Answer:** Sol.

A is neither interior of the figure nor exterior of triangle. It is a vertex.

NCERT Solutions for Class 6 Maths Exercise 4.4

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

(b) Write the names of seven angles.

(c) Write the names of sic line segments.

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

**Answer:**

(a) The three triangles are: ΔABC,ΔABC,ΔABD,ΔABD,ΔADCΔADC

(b) Angles are: ∠∠ADB, ∠∠ADC, ∠∠ABD, ∠∠ACD, ∠∠BAD, ∠∠CAD, ∠∠BAC

(c) Line segments are: AB¯¯¯¯¯¯¯,AB¯,AC¯¯¯¯¯¯¯,AC¯,AD¯¯¯¯¯¯¯¯,AD¯,BD¯¯¯¯¯¯¯,BD¯,DC¯¯¯¯¯¯¯,DC¯,BC¯¯¯¯¯¯¯BC¯

(d) Triangles having common ∠∠B: ΔABC,ΔABC,ΔABD,

**(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.

**Answer:**

(a) O is the centre.

(b) Three radii: OA, OB and OC

(c) A diameter: AC

(d) A chord: ED

(e) Interior points: O, P

(f) Exterior point: Q

(g) A sector: OAB

(h) A segment:

NCERT Solutions for Class 6 Maths Exercise 4.5

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

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

**Answer:** (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.

**Answer: **Sol.

NCERT Solutions for Class 6 Maths Exercise 4.5

**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.

**Answer:** (a) True

(b) True