CBSE Class 8

These NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry InText Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry InText Questions

Try These (Page No. 67)

Question 1.
How will you construct a rectangle PQRS if you know only the lengths PQ and QR?

Solution:
A rectangle can be constructed by taking PQ as the length making an angle 90° at Q and cutting off QR, the breadth from the ray QY. The remaining two points R and S can be located by taking P and R as centres and radii as QR and PQ respectively to draw arcs to intersect at S. Thus, PQRS is the required rectangle.

Question 2.
Construct the kite EASY if AY = 8 cm, EY = 4 cm and SY = 6 cm (Fig 4.26). Which properties of the kite did you use in the process?

Solution:
Following properties have been used in constructing the KITE:
(i) Diagonals are at right angles.
(ii) One of the diagonal bisects the other.
(iii) Pairs of consecutive sides are equal.
Steps of construction:

I. Draw a line segment AY = 8 cm.
II. Draw PQ, the perpendicular bisector of AY such that it meets AY at O.
III. We cannot locate a point E on PQ at 4 cm from Y and A, i.e., EY = 4 cm = EA is not possible.
IV. It is possible only when E and O coincide. In that case, the kite does not exist.

These NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry Ex 4.5 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry Exercise 4.5

Draw the following.

Question 1.
The square READ with RE = 5.1 cm.
Solution:

Steps of construction:
I. Draw a line segment RE = 5.1 cm.
II. At E, draw \(\overrightarrow{\mathrm{EX}}\), such that ∠REX = 90°.
III. From \(\overrightarrow{\mathrm{EX}}\), cut-off \(\overrightarrow{\mathrm{EA}}\) = 5.1 cm.
IV. With centre at A, draw an arc above RE of radius = 5.1 cm.
V. With centre at R, and radius = 5.1 cm, draw another arc to intersect the previous arc at D.
VI. Join DA and DR. Thus, READ is the required square.

Question 2.
A rhombus whose diagonals are 5.2 cm and 6.4 cm long.
Solution:

Note: The diagonals of a rhombus bisect each other at right angles.
Steps of Construction:
I. Draw a line segment AC = 5.2 cm.
II. Draw \(\overrightarrow{\mathrm{XY}}\), the perpendicular bisector of AC.
III. From XY, cut-off OD = \(\frac{1}{2}\) × (6.4 cm) = 3.2 cm.
IV. Similarly, cut-off OB = \(\frac{1}{2}\) × (6.4 cm) = 3.2 cm.
V. Join AD, DC, CB, and BA. Thus, ABCD is the required rhombus.

Question 3.
A rectangle with adjacent sides of length 5 cm and 4 cm.
Solution:

Steps of Construction:
I. Draw a line segment PQ = 5 cm
II. At Q draw \(\overrightarrow{\mathrm{QX}}\) such that ∠PQX = 90°
III. From \(\overrightarrow{\mathrm{QX}}\), cut-off QR = 4 cm.
IV. With centre R and radius = 5 cm draw an arc.
V. With centre P and radius = 4 cm draw an arc to intersect the previous arc at S.
VI. Join RQ and RS. Thus, PQRS is the required rectangle.

Question 4.
A parallelogram OKAY where OK = 5.5 cm and KA = 4.2 cm. Is it unique?
Solution:

Steps of Construction:
I. Draw a line segment OK = 5.5 cm.
II. At K, draw a ray \(\overrightarrow{\mathrm{KX}}\).
III. From \(\overrightarrow{\mathrm{KX}}\), cut-off KA = 4.2 cm.
IV. With centre at A and radius = 5.5 cm draw an arc above OK.
V. With centre O and radius = 4.2 cm, draw another arc to intersect the previous arc at Y.
VI. Join OY and AY. Thus, OKAY is the required parallelogram.

These NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry Ex 4.4 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry Exercise 4.4

Question 1.
Construct the following quadrilaterals.
(i) Quadrilateral DEAR
DE = 4 cm
EA = 5 cm
AR = 4.5 cm
∠E = 60°
∠A = 90°

(ii) Quadrilateral TRUE
TR = 3.5 cm
RU = 3 cm
UE = 4 cm
∠R = 75°
∠U = 120°
Solution:
(i)

Steps of construction:
I. Draw a line segment DE = 4 cm.
II. At E, draw \(\overrightarrow{\mathrm{EX}}\) such that ∠DEX = 60°.
III. From \(\overrightarrow{\mathrm{EX}}\), cut-off EA = 5 cm.
IV. At A, draw ray \(\overrightarrow{\mathrm{AY}}\) such that ∠EAY = 90°.
V. From \(\overrightarrow{\mathrm{AY}}\), cut-off AR = 4.5 cm.
VI. Join R and D. Thus, DEAR is the required quadrilateral.

(ii)

Steps of construction:
I. Draw a line segment \(\overrightarrow{\mathrm{TR}}\) = 3.5 cm.
II. At R, draw a ray \(\overrightarrow{\mathrm{RX}}\), such that ∠TRX = 75°
III. From \(\overrightarrow{\mathrm{RX}}\), cut-off RU = 3 cm.
IV. At U, draw \(\overrightarrow{\mathrm{UY}}\) such that ∠RUY = 120°.
V. From UY, cut-off \(\overrightarrow{\mathrm{UE}}\) = 4 cm.
VI. Join E and T. Thus, TRUE is the required quadrilateral.

These NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry Ex 4.3 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry Exercise 4.3

Question 1.
Construct the following quadrilaterals:
(i) Quadrilateral MORE
MO = 6 cm
OR = 4.5 cm
∠M = 60°
∠O = 105°
∠R = 105°

(ii) Quadrilateral PLAN
PL = 4 cm
∠A = 6.5 cm
∠P = 90°
∠A = 110°
∠N = 85°

(iii) Parallelogram HEAR
HE = 5 cm
EA = 6 cm
∠R = 85°

(iv) Rectangle OKAY
OK = 7 cm
KA = 5 cm
Solution:
(i)

Steps of construction:
I. Draw a line segment MO = 6 cm.
II. At M, draw \(\overrightarrow{\mathrm{MX}}\), such that ∠OMX = 60°
III. At O, draw \(\overrightarrow{\mathrm{OY}}\), such that ∠MOY = 105°
IV. From \(\overrightarrow{\mathrm{OY}}\), cut off OR = 4.5 cm.
V. At R, draw RZ, such that ∠ORZ = 105°. Let \(\overrightarrow{\mathrm{RZ}}\) intersects \(\overrightarrow{\mathrm{MX}}\) at E. Thus, MORE is the required quadrilateral.

(ii)

Steps of construction:
I. Draw a line segment PL = 4 cm
II. At L, draw \(\overrightarrow{\mathrm{LX}}\) such that ∠PLX = 75°
III. From \(\overrightarrow{\mathrm{LX}}\), cut off LA = 6.5 cm
IV. At A, draw \(\overrightarrow{\mathrm{AY}}\) such that ∠LAY = 110°
V. At P, draw \(\overrightarrow{\mathrm{PZ}}\) such that ∠LPZ = 90°. Let \(\overrightarrow{\mathrm{PZ}}\) and \(\overrightarrow{\mathrm{AY}}\) intersect at N. Thus, PLAN is required quadrilateral.

(iii)

Steps of Construction:
I. Draw a line segment \(\overrightarrow{\mathrm{HE}}\) = 5 cm
II. At E, draw \(\overrightarrow{\mathrm{EX}}\) such that ∠HEA = 85°
III. From \(\overrightarrow{\mathrm{EX}}\), cut-off EA = 6 cm.
IV. With centre at A and radius = 5 cm, draw an arc.
V. With centre at H and radius = 6 cm, draw an arc such that it intersects the previous arc at R.
VI. Join RA and RH. Thus, HEAR is the required parallelogram.

(iv)

Steps of Construction:
I. Draw a line segment OK = 7 cm.
II. At O, draw \(\overrightarrow{\mathrm{OP}}\) such that ∠KOP = 90°.
III. From \(\overrightarrow{\mathrm{OP}}\), cut-off \(\overrightarrow{\mathrm{OY}}\) = 5 cm.
IV. At K, draw \(\overrightarrow{\mathrm{KQ}}\) such that ∠OKQ = 90°
V. From \(\overrightarrow{\mathrm{KQ}}\), cut-off \(\overrightarrow{\mathrm{KA}}\) = 5 cm.
VI. Join AY. Thus, OKAY is the required rectangle.

These NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry Ex 4.2 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry Exercise 4.2

Question 1.
Construct the following quadrilaterals.
(i) Quadrilateral LIFT
LI = 4 cm
IF = 3 cm
TL = 2.5 cm
LF = 4.5 cm
IT = 4 cm

(ii) Quadrilateral GOLD
OL = 7.5 cm
GL = 6 cm
GD = 6 cm
LD = 5 cm
OD = 10 cm

(iii) Rhombus BEND
BN = 5.6 cm
DE = 6.5 cm
Solution:
(i)

Steps of Construction:
I. Draw a line segment LI = 4 cm.
II. With centre at I and radius = 4 cm, draw an arc.
III. With centre at L and radius = 2.5 cm, draw another arc to intersect the previous arc at T.
IV. Join TI and TL.
V. With centre at L and radius = 4.5 cm, draw an arc on the side opposite to that of L.
VI. With centre at I and radius = 3 cm, draw another arc to intersect the previous arc at F.
VII. Join FL and FI.
Thus, LIFT is the required quadrilateral.

(ii)

Steps of construction:
I. Draw a line segment LD = 5 cm.
II. With centre at L and radius = 6 cm, draw an arc.
III. With centre at D and radius = 6 cm, draw another arc to intersect the previous arc at G.
IV. Join GL and GD.
V. With centre at D and radius = 10 cm, draw an arc.
VI. With centre at L at radius = 7.5 cm, draw another arc to intersect the previous arc at O.
VII. Join OL and OG.
Thus, GOLD is the required quadrilateral.

(iii)

Steps of construction:
I. Draw a line segment DE = 6.5 cm.
II. Draw perpendicular bisector of DE such that M is the mid-point of DE.
III. With centre M and radius = 2.8 cm, draw arcs to intersect the perpendicular bisector at B and N.
IV. Join ND, NE, BE, and BD.
Thus, BEND is the required rhombus.

These NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry Ex 4.1 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry Exercise 4.1

Question 1.
Construct the following quadrilaterals.
(i) Quadrilateral ABCD
AB = 4.5 cm
BC = 5.5 cm
CD = 4 cm
AD = 6 cm
AC = 7 cm

(ii) Quadrilateral JUMP
JU = 3.5 cm
UM = 4 cm
MP = 5 cm
PJ = 4.5 cm
PU = 6.5 cm

(iii) Parallelogram MORE
OR = 6 cm
RE = 4.5 cm
EO = 7.5 cm

(iv) Rhombus BEST
BE = 4.5 cm
ET = 6 cm
Solution:
(i)

Steps of Construction:
I. Draw a line segment AB = 4.5 cm.
II. With centre at A and radius = 7 cm, draw an arc.
III. With centre at B and radius = 5.5 cm, draw another arc to intersect the previous arc at C.
IV. With centre at A and radius = 6 cm, draw an arc on the side opposite to that of B.
V. With centre at C and radius = 4 cm, draw another arc to intersect the previous arc at D.
VI. Join AC, BC, DA, and DC. Thus, ABCD is the required quadrilateral.

(ii)

Steps of Construction:
I. Draw a line segment JU = 3.5 cm.
II. With centre at U and radius UP = 6.5 cm, draw an arc.
III. With centre at J and radius = 4.5 cm, draw another arc to intersect the previous arc at P.
IV. With centre at U and radius = 4 cm, draw an arc on the side opposite to that of J.
V. With centre at P and radius = 4 cm, draw another arc intersecting the previous arc at M.
VI. Join PJ, PU, PM, and UM. Thus, JUMP is the required quadrilateral.

(iii)

Note: In a parallelogram opposite sides are equal.
Steps of Construction:
I. Draw a line segment MO = 4.5 cm
II. With centre O and radius = 7.5 cm, draw an arc.
III. With centre M and radius = 6 cm, draw another arc to intersect the previous arc at E.
IV. With centre at O and radius = 6 cm, draw an arc on the side opposite to E
V. With centre at E and radius = 4.5 cm, draw another arc to intersect the previous arc at R.
VI. Join OR, RE, EO, and EM. Thus, MORE is the required parallelogram.

(iv)

Steps of constructions:
I. Draw a line segment BE = 4.5 cm.
II. With centre at E and radius = 6 cm, draw an arc.
III. With centre at B and radius = 4.5 cm, draw another arc to intersect the previous arc at T.
Note: All 4 sides of a rhombus are equal.
IV. Join TB and TE.
V. With centre at T and radius = 4.5 cm, draw an arc on the side opposite to that of B.
VI. With centre at E and radius = 4.5 cm, draw another arc to intersect the previous arc at S.
VII. Join ST and SE. Thus, BEST is the required rhombus.