NCERT Solutions Class 6 Maths Chapter 4

Q.1 Use the figure to name:
(a) Five points
(b) A line
(c) Four rays
(d) Five line segments

Ans.

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

$\left(\mathrm{b}\right)\text{A line is}\overleftrightarrow{\text{BD}}.$ $$

$\left(\text{c}\right)\mathrm{}\text{Four rays are}:\overrightarrow{\mathrm{OB}},\overrightarrow{\mathrm{OE}},\overrightarrow{\mathrm{OD}},\overrightarrow{\mathrm{ED}}\text{and}\overrightarrow{\text{EB}}$

$\left(\text{d}\right)\text{Five line segments are}:\overline{\text{DE}},\overline{\text{EO}},\overline{\text{OB}},\overline{\text{EB}}\text{and}\overline{\text{DB}}.$

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

Ans.

\begin{array}{l}\text{Twelve ways to represent line are}:\overleftrightarrow{\text{AB}}\text{,}\overleftrightarrow{\text{AC}}\text{,}\overleftrightarrow{\text{AD}}\text{,}\overleftrightarrow{\text{BC}}\text{,}\overleftrightarrow{\text{BD}}\text{,}\overleftrightarrow{\text{CD}}\text{,}\\ \overleftrightarrow{\text{DA}}\text{,}\overleftrightarrow{\text{DB}}\text{,}\overleftrightarrow{\text{DC}}\text{,}\overleftrightarrow{\text{CB}}\text{,}\overleftrightarrow{\text{CA}}\end{array}

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.

Ans.

$\begin{array}{l}\left(\text{a}\right)\text{Line containing E is}\overleftrightarrow{\text{AE}}\text{.}\\ \left(\mathrm{b}\right)\text{Line passing through A is}\overleftrightarrow{\text{AE}}\text{.}\\ \left(\mathrm{c}\right)\text{\hspace{0.17em} Line on which O lies is}\overleftrightarrow{\text{BC}}\text{.}\\ \left(\mathrm{d}\right)\text{\hspace{0.17em} Two pairs of intersecting lines are:}\overleftrightarrow{\text{OC}}\text{and}\overleftrightarrow{\text{BE}},\overrightarrow{\text{AE}}\text{and}\overrightarrow{\text{EF}}.\end{array}$

Q.4 How many lines can pass through
(a) one given point?
(b) two given points?

Ans.

(a) Many lines can pass through one point.
(b) Only one line can pass through two given points.

Q.5

$\begin{array}{l}\mathrm{Draw}\mathrm{arough}\mathrm{figure}\mathrm{and}\mathrm{label}\mathrm{suitably}\mathrm{in}\mathrm{each}\mathrm{of}\mathrm{the}\\ \mathrm{following}\mathrm{cases}:\\ \left(\mathrm{a}\right)\mathrm{Point}\mathrm{P}\mathrm{lieson}\overline{\mathrm{AB}}.\\ \left(\mathrm{b}\right)\overleftrightarrow{\mathrm{XY}}\mathrm{and}\overleftrightarrow{\mathrm{PQ}}\mathrm{intersect}\mathrm{at}\mathrm{M}.\\ \left(\mathrm{c}\right)\mathrm{Line}\mathrm{l}\mathrm{contains}\mathrm{E}\mathrm{and}\mathrm{F}\mathrm{but}\mathrm{not}\mathrm{D}.\\ \left(\mathrm{d}\right)\overleftrightarrow{\mathrm{OP}}\mathrm{and}\overleftrightarrow{\mathrm{OQ}}\mathrm{meet}\mathrm{at}\mathrm{O}.\end{array}$

Ans.

(a)

(b)

(c)

(d)

Q.6

$\begin{array}{l}\mathrm{Consider}\mathrm{the}\mathrm{following}\mathrm{figure}\mathrm{of}\mathrm{line}\overleftrightarrow{\mathrm{MN}}.\mathrm{Say}\mathrm{whether}\\ \mathrm{following}\mathrm{statements}\mathrm{are}\mathrm{true}\mathrm{or}\mathrm{false}\mathrm{in}\mathrm{context}\mathrm{of}\mathrm{the}\\ \mathrm{given}\mathrm{figure}.\\ \left(\mathrm{a}\right)\mathrm{Q},\mathrm{M},\mathrm{O},\mathrm{N},\mathrm{Pare}\mathrm{points}\mathrm{on}\mathrm{the}\mathrm{line}\overleftrightarrow{\mathrm{MN}}.\\ \left(\mathrm{b}\right)\mathrm{M},\mathrm{O},\mathrm{N}\mathrm{are}\mathrm{points}\mathrm{on}\mathrm{a}\mathrm{line}\mathrm{segment}\overleftrightarrow{\mathrm{MN}}.\\ \left(\mathrm{c}\right)\mathrm{M}\mathrm{and}\mathrm{N}\mathrm{are}\mathrm{end}\mathrm{points}\mathrm{of}\mathrm{line}\mathrm{segment}\overleftrightarrow{\mathrm{MN}}.\\ \left(\mathrm{d}\right)\mathrm{O}\mathrm{and}\mathrm{N}\mathrm{are}\mathrm{end}\mathrm{points}\mathrm{of}\mathrm{line}\mathrm{segment}\overline{\mathrm{OP}}.\\ \left(\mathrm{e}\right)\mathrm{M}\mathrm{is}\mathrm{one}\mathrm{of}\mathrm{the}\mathrm{end}\mathrm{points}\mathrm{of}\mathrm{line}\mathrm{segment}\overline{\mathrm{QO}}.\\ \left(\mathrm{f}\right)\mathrm{M}\mathrm{is}\mathrm{point}\mathrm{on}\mathrm{ray}\overrightarrow{\mathrm{OP}}.\\ \left(\mathrm{g}\right)\mathrm{Ray}\overrightarrow{\mathrm{OP}}\mathrm{is}\mathrm{different}\mathrm{from}\mathrm{ray}\overrightarrow{\mathrm{QP}}.\\ \left(\mathrm{h}\right)\mathrm{Ray}\overrightarrow{\mathrm{OP}}\mathrm{is}\mathrm{same}\mathrm{as}\mathrm{ray}\overrightarrow{\mathrm{OM}}.\\ \left(\mathrm{i}\right)\mathrm{Ray}\overrightarrow{\mathrm{OM}}\mathrm{is}\mathrm{not}\mathrm{opposite}\mathrm{to}\mathrm{ray}\overrightarrow{\mathrm{OP}}.\\ \left(\mathrm{j}\right)\mathrm{O}\mathrm{is}\mathrm{not}\mathrm{an}\mathrm{initial}\mathrm{point}\mathrm{of}\overrightarrow{\mathrm{OP}}.\\ \left(\mathrm{k}\right)\mathrm{N}\mathrm{is}\mathrm{the}\mathrm{initial}\mathrm{point}\mathrm{of}\overrightarrow{\mathrm{NP}}\mathrm{and}\overrightarrow{\mathrm{NM}}.\end{array}$

Ans.

$\begin{array}{l}\left(\text{a}\right)\text{True},\text{Q},\text{M},\text{O},\text{N},\text{P are points on the line\hspace{0.17em}}\overleftrightarrow{\mathrm{MN}}.\\ \left(\mathrm{b}\right)\text{True},\text{M, O, N are points on a line segment}\overleftrightarrow{\text{MN}}\text{.}\\ \left(\mathrm{c}\right)\text{\hspace{0.17em}True},\text{M and N are end points on a line segment}\overleftrightarrow{\text{MN}}\text{.}\\ \left(\mathrm{d}\right)\mathrm{False},\text{O and P are end points of line segment}\overline{\text{OP}}\text{.}\\ \left(\mathrm{e}\right)\mathrm{False},\text{Q and O are the end points of line segment}\overline{\text{OQ}}\text{.}\\ \left(\mathrm{f}\right)\mathrm{False},\text{N is a point of ray}\overrightarrow{\text{OP}}\text{.}\\ \left(\mathrm{g}\right)\text{True, both rays have different starting point.}\\ \left(\mathrm{h}\right)\mathrm{False},\text{both are opposite rays.}\\ \left(\mathrm{i}\right)\mathrm{False},\mathrm{ray}\overrightarrow{\mathrm{OM}}\mathrm{isoppositetoray}\overrightarrow{\mathrm{OP}}.\\ \left(\mathrm{j}\right)\mathrm{False},\text{O is initial point of}\overrightarrow{\mathrm{OP}}.\\ \left(\mathrm{k}\right)\text{True, N is initial point of both rays.}\end{array}$

Q.7 Classify the following curves as
(i) Open or
(ii)Closed.

Ans.

Q.8 Draw rough diagrams to illustrate the following:
(a) Open curve
(b) Closed curve.

Ans.

Open curves are: (a) and (c).
Closed curves are: (b), (d) and (e).

Q.9 Draw any polygon and shade its interior.

Ans. The required pentagon is shaded as given below:

Q.10 Consider the given figure and answer the questions:
(a) Is it a curve?
(b) Is it closed?

Ans.

(a) Yes, it is a curve.
(b) Yes, it is closed.

Q.11 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.

Ans.

(a)

(b)

(c) A polynomial with two sides is not possible.

Q.12 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?

Ans.

Point A is on the triangle ABC; it is neither in its exterior nor in its interior.

Q.13 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?

Ans.

Diagonals are AC and BD. Meeting point of diagonals is in the interior of the quadrilateral.

Q.14 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

Ans.

(a) O is the centre of the circle.
(b) Three radii are: OA, OB and OC.
(c) A diameter is AC.
(d) A chord is ED.
(e) Two points in the interior are: O and P.
(f) A point in the exterior is Q.
(g) OAB is a sector.
(h) EBD is a segment.

Q.15 (a) Is every diameter of a circle also a chord?
(b) Is every chord of a circle also a diameter?

Ans.

(a) Yes, every diameter of a circle is also a chord.
(b) No, every chord of a circle is not a diameter.
Only a chord which passes through the centre of circle is called diameter.

Q.16 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

Ans.

(a) Circle with centre O is given below:

(b) Circle with radius OA is given below:

(c) Circle with diameter AB is given below:

(d) Circle with sector AOB is given below:

(e) Circle with segment AB is given below:

(f) Point A is in the interior of circle is shown below:

(g) A point in its exterior of circle is shown below:

(h) An arc is shown below:

Q.17 Say true or false:
(a) Two diameters of a circle will necessarily intersect.
(b) The centre of a circle is always in its interior.

Ans.

(a) True, two diameters of a circle will necessarily intersect.
(b) True, centre of a circle is always in its interior.

Q.18 Name the angles in the given figure.

Ans.

Four angles in the given figure are:
∠DAB, ∠ABC, ∠BCD and ∠CDA.

Q.19 In the given diagram, name the point(s)
(a) In the interior of ∠DOE
(b) In the exterior of ∠EOF
(c) On ∠EOF

Ans.

(a) Point A is in the interior of ∠DOE.
(b) Points A, C and D are in the exterior of ∠EOF.
(c) Points E, B, O and F lie on ∠EOF.

Q.20 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.

Ans.

(a) ∠ABC and ∠CBD have B as a common point.

(b) ∠ABC and ∠ABD have A and B as two common points.

(c) ∠ABC and ∠ACB have three common points.

(d) ∠DAC and ∠EPD have four common points i.e. B, C, D and E.

Q.21 (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 ∠B as common?

Ans.

(a) Three triangles are ΔABD, ΔADC and ΔABC.
(b) Seven angles are: ∠ABC, ∠ACB, ∠BAC, ∠BAD, ∠CAD, ∠ADB and ∠ADC.
(c) Six line segments are:

\overline{\text{AB}},\overline{\text{AC}},\overline{\text{BD}},\overline{\text{DC}},\overline{\text{BC}}\text{and}\overline{\text{AD}}.

(d) ΔABC and ΔABD have ∠B as common.

Q.22 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.

Ans.

(a) Two pairs of opposite sides are:
KL and MN, LM and KN.
(b) Two pairs of opposite angles are:
∠LKN and ∠LMN,
∠KLM and ∠KNM.
(c) Two pairs of adjacent sides are:
KL and LM, LM and MN.
(d) Two pairs of adjacent angles are:
∠LMN and ∠MNK,
∠KLM and ∠LMN.