## NCERT Solutions Class 6 Maths## Chapter 4: Basic Geometrical Ideas## Exercise 4.1
For example, OB, OE, OD, OC DE, DO, DB EO, ED, EB
There are multiple rays in the above diagram. OB, OE, OD, OC DE, DO, DB EO, ED, EB
OB, OE, OD, OC DE, DO, DB EO, ED, EB
- AB
- AC
- AD
- BA
- BC
- BD
- CA
- CB
- CD
- DA
- DB
- DC
For example, AE, BE, DE, FE
For example, AE, AD, and AB
Pair 1: CO and AE Pair 2: AE and EF
There are multiple names of two pairs of these intersecting lines. For example, 1. OC and EA EA and FE 2. OC and AB EF and DE 3. OC and AD FE and EB
(a) one given point?
(b) two given points?
(a) Point P lies on AB.
(b) XY and PQ intersect at M.
(c) Line l contains E and F but not D.
(d) OP and OQ meet at O.
(a) Q, M, O, N, P are points on the line MN.
(b) M, O, N are points on a line segment MN .
(c) M and N are end points of line segment MN .
(d) O and N are end points of line segment OP .
(e) M is one of the end points of line segment QO.
(f) M is point on ray OP.
(g) Ray OP is different from ray QP.
(h) Ray OP is same as ray OM.
(i) Ray OM is not opposite to ray OP.
(j) O is not an initial point of OP.
(k) N is the initial point of NP and NM.
## Exercise 4.2
(a) Open curve (b) Closed curve (c) Open curve (d) Closed curve (e) Closed curve
Open curves are the curves that are joined end to end. It means the end points of the curve are joined together. Closed curves are the curves that have open ends. It means the end points of the curve are different.
(a) Open curve
(b) Closed curve.
We can draw any type of open or closed curve.
A polygon is a figure made of three or more line segments. There are different types of polygons.
- It is a polygon with six sides.
- It is a polygon with three sides.
- It is a polygon with five sides.
(a) Is it a curve?
It is a curve because a curve has line segments linked end to end. (b) Is it closed?
(a) A closed curve that is not a polygon.
(b) An open curve made up entirely of line segments.
A curve has line segments linked end to end. A polygon is a closed figure made of three or more line segments. A curve can be made of different types of curves and line segments, while a polygon is only made of line segments. (c) A polygon with two sides.
Not possible. We cannot make a closed figure made of two line segments.
## Exercise 4.3
∠ADC or ∠D or ∠CDA ∠DCB or ∠C or ∠BCD ∠CBA or ∠B or ∠ABC ∠BAD or ∠A or ∠DAB
(a) In the interior of ∠DOE
(b) In the exterior of ∠EOF
(c) On ∠EOF
(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.
## Exercise 4.4
A lies neither on the exterior nor interior.
∠ABD or ∠DBA or ∠B ∠BDA or ∠ADB ∠ADC or ∠CDA ∠DCA or ∠ACD or ∠C ∠CAD or ∠DAC ∠DAB or ∠BAD ∠CAB or ∠BAC or ∠A
AB or BA BD or DB DC or CD AC or CA AD or DA BC or CB ## Note: The names of the angles, line segments, and traingle can be both clockwise or anti-clockwise. We can select any option.
## Exercise 4.5
The meeting point of the quadrilateral lies in the interior of the traingle.
State, (a) two pairs of opposite sides
KL and NM KN and ML (b) two pairs of opposite angles
∠K and ∠M ∠L and ∠N (c) two pairs of adjacent sides
NM and LM LK and KN Or MN and NK KL and NM (d) two pairs of adjacent angles
∠K and ∠L ∠M and ∠N Or ∠K and ∠N ∠M and ∠L ## Exercise 4.6
(a) the centre of circle
O is the center point of the circle. (b) three radii
OC, OA, and OB are three radii of the circle. Radius = Diameter/2 (c) a diameter
A diameter always pass through the center of the circle touching the two points on the circumference. Hence, AC is the only diameter in the above figure. (d) a chord
A chord is a line segment touching the two points on the circumference. (e) two points in the interior
O and P are the two points lying inside the circle. (f) a point in the exterior
Q is the point lying outside the circle. (g) a sector
AOB or OAB or OBA AOB is the sector of the above circle. It is represented by the shaded portion. (h) a segment
ED is the segment of the above circle. It is also represented by the shaded portion. 2.
(a) Two diameters of a circle will necessarily intersect.
(b) The centre of a circle is always in its interior.
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