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Exercise 4.3 - Chapter 4 Practical Geometry class 8 ncert solutions Maths - SaraNextGen [2024]


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

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

Answer:

(i)

(1)A rough sketch of this quadrilateral can be drawn as follows.

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/67/3275/Chapter%204_html_4377f1db1.jpg

(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.

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/67/3275/Chapter%204_html_3c7a185d1.jpg

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

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/67/3275/Chapter%204_html_93085761.jpg

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

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/67/3275/Chapter%204_html_45e2c64d1.jpg

MORE is the required quadrilateral.

(1)The sum of the angles of a quadrilateral is 360°.(ii)

In quadrilateral PLAN, ∠P + ∠L + ∠A + ∠N = 360°

90° + ∠L + 110° + 85° = 360°

285° + ∠L = 360°

∠L = 360° − 285° = 75°

(2)A rough sketch of this quadrilateral is as follows.

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/67/3275/Chapter%204_html_m24635ce31.jpg

(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.

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/67/3275/Chapter%204_html_m7709ba981.jpg

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

https://img-nm.mnimgs.com/img/study_content/editlive_ncert/75/2012_06_14_13_10_53/6.2_8293413547146715404.png

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

https://img-nm.mnimgs.com/img/study_content/editlive_ncert/75/2012_06_14_13_20_37/zlhhufry_8552160521691941484.png

PLAN is the required quadrilateral.

(iii)

(1)Firstly, a rough sketch of this quadrilateral is as follows.

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/67/3275/Chapter%204_html_m1f4d39f71.jpg

(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.

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/67/3275/Chapter%204_html_m1263ce731.jpg

(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.

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/67/3275/Chapter%204_html_23830c2f1.jpg

4. Join R to H and A.

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/67/3275/Chapter%204_html_715a87a01.jpg

HEAR is the required quadrilateral.

(iv)

(1)A rough sketch of this quadrilateral is drawn as follows.

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/67/3275/Chapter%204_html_m5c3f30701.jpg

(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.

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/67/3275/Chapter%204_html_m35ac6f9a1.jpg

(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.

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/67/3275/Chapter%204_html_56ffd4471.jpg

(4) Join Y to A and O.

https://img-nm.mnimgs.com/img/study_content/curr/1/8/5/67/3275/Chapter%204_html_m2238f1d11.jpg

OKAY is the required quadrilateral.

Also Read : Exercise-4.4-Chapter-4-Practical-Geometry-class-8-ncert-solutions-Maths

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