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# Basic geometrical ideas

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

(a)Five points

(b)A line

(c)Four rays

(d)Five line segments

(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 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¯

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.

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

(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

Closed curves

NCERT Solutions for Class 6 Maths Exercise 4.2

###### 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.

(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.

(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.

(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?

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?

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

###### Question 1.From the figure, identify:

(a)The centre of circle.

(c)A diameter.

(d)A chord.

(e)Two points in the interior.

(f)A point in the exterior.

(g)A sector.

(h)A segment.

(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.

(c)A diameter.

(d)A sector.

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.

(b) True

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