Practical Geometry - Solutions 3
CBSE Class –VIII Mathematics
NCERT Solutions
CHAPTER - 4
Practical Geometry (Ex. 4.3)
NCERT Solutions
CHAPTER - 4
Practical Geometry (Ex. 4.3)
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, LA = 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
Ans. (i) Given: MO = 6 cm, OR = 4.5 cm,
∠M = 60°, ∠O = 105°, ∠R = 105°
To construct: A quadrilateral MORE
Steps of construction:
(a) Draw a line segment MO = 6 cm.
(b) Construct ∠R = 105° and taking radius 4.5 cm, draw an arc taking O as centre, which intersects at R.
(c) Also construct an angle 105° at R and produce the side RE.
(d) Construct another angle of 60° at point M and produce the side ME. Both sides ME and RE intersect at E.
It is the required quadrilateral MORE.
(ii) Given: PL = 4 cm, LA = 6.5 cm,
(ii) Given: PL = 4 cm, LA = 6.5 cm,
∠P = 90°, ∠A = 110°, ∠N = 85°
To construct: A quadrilateral PLAN
To find: ∠L = 360° - (90° + 85° + 110°) = 360° - 285° = 75°
Steps of construction:
(a) Draw a line segment PL = 4 cm.
(b) Construct angle of 90° at P and produce the side PN.
(c) Construct angle of 75° at L and with L as centre, draw an arc of radius 6 cm, which intersects at A.
|(d) Construct ∠A = 110° at A and produce the side AN which intersects PN at N.
(b) Construct angle of 90° at P and produce the side PN.
(c) Construct angle of 75° at L and with L as centre, draw an arc of radius 6 cm, which intersects at A.
|(d) Construct ∠A = 110° at A and produce the side AN which intersects PN at N.
It is the required quadrilateral PLAN.
(iii) Given: HE = 5 cm, EA = 6 cm, ∠R = 85°
(iii) Given: HE = 5 cm, EA = 6 cm, ∠R = 85°
To construct: A parallelogram HEAR
To find: ∠H = 180° - 85° = 95°
[
Sum of adjacent angle of ||gm is 180°]
Sum of adjacent angle of ||gm is 180°]
Steps of construction:
(a) Draw a line segment HE = 5 cm.
(b) Construct ∠H = 95° and draw an arc of radius 6 cm with centre H. It intersects AR at R.
(c) Join RH.
(d) Draw ∠R = ∠E = 85° and draw an arc of radius 6 cm with E as a centre which intersects RA at A.
(e) Join RA.
(b) Construct ∠H = 95° and draw an arc of radius 6 cm with centre H. It intersects AR at R.
(c) Join RH.
(d) Draw ∠R = ∠E = 85° and draw an arc of radius 6 cm with E as a centre which intersects RA at A.
(e) Join RA.
It is the required parallelogram HEAR.
(iv) Given: OK = 7 cm, KA = 5 cm
(iv) Given: OK = 7 cm, KA = 5 cm
To construct: A rectangle OKAY
Steps of construction:
(a) Draw a line segment OK = 7 cm.
(b) Construct angle 90° at both points O and K and produce these sides.
(c) Draw two arcs of radius 5 cm from points O and K respectively. These arcs intersect at Y and A.
(d) Join YA.
(b) Construct angle 90° at both points O and K and produce these sides.
(c) Draw two arcs of radius 5 cm from points O and K respectively. These arcs intersect at Y and A.
(d) Join YA.
It is the required rectangle OKAY.
