### 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°]

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.