NCERT solutions for class 6 mathematics -Exercise Solutions

Chapter 04-Basic Geometrical Ideas

NCERT Book Page Number-74
Q.1. Use the figure to name:

 

(a) Five points
(b) A line
(c) Four rays
(d) Five line segments
Answer:
(a) The five points are D, E, O, B, and C.
(b) $\overline{BD}$
(c) $\overline{OD}$, $\overline{OB}$,$\overline{OC}$, $\overline{OE}$
(d) $\overline{DE}$,$\overline{EO}$,$\overline{OB}$,$\overline{OC}$,$\overline{BE}$
Q.2. Name the line given in all possible (twelve) ways, choosing only two letters at a time from the four given.

Answer:
$\overline{AB}$,$\overline{BC}$,$\overline{CD}$,$\overline{BA}$,$\overline{CB}$,$\overline{DC}$,$\overline{AD}$,$\overline{DA}$,$\overline{AC}$,$\overline{CA}$,$\overline{BD}$,$\overline{DB}$

NCERT Book Page Number-75
Q.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) $\overline{AE}$
(b) $\overline{AE}$
(c) $\overline{OC}$
(d) $\overline{OC}$ and $\overline{AE}$, $\overline{AE}$ and $\overline{EF}$
Q.4. How many lines can pass through (a) one given point? (b) Two given points?
Answer:
(a) Infinite number of lines can pass through a single 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 $\overline{AB}$.
(b) $\overline{XY}$ and $\overline{PQ}$ intersect at M.
(c) Line l contains E and F but not D.
(d) $\overline{OP}$ and $\overline{OQ}$ meet at O.
Answer:
(a)

 

 Q.5. Consider the following figure of line $\overline{MN}$. Say whether following statements are true or false in context of the given figure.


(a) Q, M, O, N, P are points on the line $\overline{MN}$.
(b) M, O, N are points on a line segment $\overline{MN}$.
(c) M and N are end points of line segment $\overline{MN}$.
(d) O and N are end points of line segment $\overline{OP}$.
(e) M is one of the end points of line segment $\overline{QO}$.
(f) M is point on ray $\overline{OP}$.
(g) Ray $\overline{OP}$is different from ray $\overline{QP}$.
(h) Ray $\overline{OP}$is same as ray $\overline{OM}$.
(i) Ray $\overline{OM}$is not opposite to ray $\overline{OP}$.
(j) O is not an initial point of $\overline{OP}$.
(k) N is the initial point of $\overline{NP}$ and $\overline{NM}$.
Answer:
(a) True
(b) True
(c) True
(d) False
(e) False
(f) False
(g) True
(h) False
(i) False
(j) False
(k) True
NCERT Book Page Number-78
Q.1. Classify the following curves as (i) Open or (ii) Closed.


Answer:
(a) Open
(b) Closed
(c) Open
(d) Closed
(e) Closed
Q.2. Draw rough diagrams to illustrate the following:
(a) Open curve (b) Closed curve.
Answer:
(a) Open curve


(b) Closed curve


Q.3. Draw any polygon and shade its interior.
Answer:


Q.4. Consider the given figure and answer the questions:
(a) Is it a curve? (b) Is it closed?


Answer:
(a) Yes
(b) Yes
Q.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)


(c) This is not possible as the polygon having the least number of sides is a triangle, which has three sides in it.
NCERT Book Page Number-80
Q.1. Name the angles in the given figure.


Answer:
$\angle BAD$, $\angle ADC$, $\angle DCB$, $\angle CBA$
Q.2. In the given diagram, name the point (s)


(a) In the interior of $\angle DOE$
(b) In the exterior of $\angle EOF$
(c) On $\angle EOF$∠EOF
Answer:
(a) A
(b) C, A, D
(c) B, E, O, F
Q.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)


$\angle COD$ and $\angle AOB$ have point O in common.
(b)


$\angle AOB$ and $\angle BOC$ have points O and B in common.
(c)


$\angle AOB$ and $\angle BOC$ have points O, E, B in common.
(d)


$\angle BOA$ and $\angle COA$ have points O, E, D, A in common.
(e)


Ray$\overline OC$ is common between $\angle BOC$ and $\angle AOC$.
NCERT Book Page Number-81
Q.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:


Point A lies on the given $\triangle ABC$.
Q.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 $\angle B$ as common?
Answer:
(a) $\triangle ABC$, $\triangle ACD$, $\triangle ADB$
(b) $\angle ABC$, $\angle ADB$, $\angle ADC$, $\angle ACB$, $\angle BAD$, $\angle CAD$, $\angle BAC$
(c)$\overline AB$, $\overline BC$, $\overline CA$,$\overline AD$, $\overline BD$,$\overline CD$
(d) $\triangle ABD$ and $\triangle ABC$
NCERT Book Page Number-82
Q.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?


Diagonals are PR and QS. They meet at point O which is in the interior of &mnSq1PQRS.
Q.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.
Answer:


(a) $\overline KL$, $\overline NM$, and $\overline KN$, $\overline ML$,
(b) $\angle KLM $ and $ angle KNM$, $ angle LKN$ and $ angle LMN$

(c) $\overline KL$, $\overline KN$, and $\overline NM$, $\overline ML$,
$\overline KL$, $\overline LM$, and $\overline NM$, $\overline NK$,
(d) $\angle K $ , $\angle L $ and $\angle M $, $\angle N $
$\angle K $ , $\angle N $ and $\angle L $, $\angle M
NCERT Book Page Number-84
Q.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
(b) $\overline OA$, $\overline OB$, $\overline OC$,
(c) $\overline AC$,
(d) $\overline ED$,
(e) O, P
(f) Q
(g) AOB (shaded region)
(h) DE (shaded region)

Q.2. (a) Is every diameter of a circle also a chord?
(b) Is every chord of circle also a diameter?
Answer:
(a) Yes. The diameter is the longest possible chord of the circle.
(b) No
Q.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

Answer:


(a) O
(b) $\overline OA$
(c) $\overline AB$
(d) COA
(e) DE
(f) O
(g) F
(h) $\widehat AC$
Q.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. They will always intersect each other at the centre of the circle.
(b) True