NCERT Solutions for class 8 Maths chapter 4 Practical geometry exercise 4.3

Exercise 4.3

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Q 1 - Ex 4.3 - Practical Geometry - NCERT Maths Class 8th - Chapter 4

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Question 1
Construct the following quadrilaterals.
(i) Quadrilateral MORE
MO = 6 cm
OR = 4.5 cm
∠M = 60°
∠O = 105°
∠R = 105°
Sol :
(Step-1)A rough sketch of this quadrilateral can be drawn as follows.

(Step-2) Draw a line segment MO of 6 cm and an angle of 105º at point O. As vertex R is 4.5 cm away from the vertex O, cut a line segment OR of 4.5 cm from this ray.

(Step-3) Again, draw an angle of 105º at point R.

(Step-4) Draw an angle of 60º at point M. Let this ray meet the previously drawn ray from R at point E.

MORE is the required quadrilateral.

(ii) Quadrilateral PLAN
PL = 4 cm
LA = 6.5 cm
∠P = 90°
∠A = 110°
∠N = 85°
Sol :
(Step-1)The sum of the angles of a quadrilateral is 360°.
In quadrilateral PLAN, ∠P + ∠L + ∠A + ∠N = 360°
90° + ∠L + 110° + 85° = 360°
285° + ∠L = 360°
∠L = 360° − 285° = 75°
(Step-2)A rough sketch of this quadrilateral is as follows.

(Step-3) Draw a line segment PL of 4 cm and draw an angle of 75º at point L. As vertex A is 6.5 cm away from vertex L, cut a line segment LA of 6.5 cm from this ray.

(Step-4) Again draw an angle of 110º at point A.

(Step-5) Draw an angle of 90º at point P. This ray will meet the previously drawn ray from A at point N.

PLAN is the required quadrilateral.


(iii) Parallelogram HEAR
HE = 5 cm
EA = 6 cm
∠R = 85°
Sol :
(Step-1)Firstly, a rough sketch of this quadrilateral is as follows.

(Step-2) Draw a line segment HE of 5 cm and an angle of 85º at point E. As vertex A is 6 cm away from vertex E, cut a line segment EA of 6 cm from this ray.

(Step-3) Vertex R is 6 cm and 5 cm away from vertex H and A respectively. By taking radius as 6 cm and 5 cm, draw arcs from point H and A respectively. These will be intersecting each other at point R.

4. Join R to H and A.

HEAR is the required quadrilateral.

(iv) Rectangle OKAY
OK = 7 cm
KA = 5 cm
Sol :
(iv)
(Step-1)A rough sketch of this quadrilateral is drawn as follows.

(Step-2) Draw a line segment OK of 7 cm and an angle of 90º at point K. As vertex A is 5 cm away from vertex K, cut a line segment KA of 5 cm from this ray.

(Step-3) Vertex Y is 5 cm and 7 cm away from vertex O and A respectively. By taking radius as 5 cm and 7 cm, draw arcs from point O and A respectively. These will be intersecting each other at point Y.

(Step-4) Join Y to A and O.

OKAY is the required quadrilateral.