Class 8 Maths NCERT Solutions for Chapter – 4 Practical Geometry Ex – 4.3

Practical Geometry

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.

Solution.
(i) Draw a rough sketch of the required quadrilateral and write down its dimensions.

Steps of Construction :

  • Draw MO = 6 cm.
  • Make ∠MOX = 105°.
  • With O as centre and radius 4.5 cm, cut off OR = 4.5 cm along OX.
  • Make ∠ORY = 105°.
  • Make ∠ZMO = 60° such that arms RY and MZ intersect at E.
    Then, MORE is the required quadrilateral.

(ii) Draw a rough sketch of the required quadrilateral PLAN and write down its dimensions.
Before taking up the construction let us find the ∠PLA which is equal to 360° – (90°+ 110°+ 85°)
= 360°-285° = 75°.

Steps of Construction :
NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry 16

  • Draw PL = 4 cm.
  • Make ∠XPL =90°.
  • Make ∠YLP = 75°.
  • With L as centre and radius 6.5 cm, cut off LA – 6.5 cm along LY.
  • Make ∠ZAL =110° and let its arm AZ intersect PX at N.
    Then, PLAN is the required quadrilateral.

(iii) We know that the opposite angles of a parallelogram are equal. Make a rough sketch of the required parallelogram as shown.

Steps of Construction :
NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry 18

  • Draw HE = 5 cm.
  • Make ∠HEX = 85°.
  • With E as centre and radius 6 cm, cut off EA = 6 cm along EX.
  • With A as centre and radius 5 cm, draw an arc.
  • With H as centre and radius 6 cm, draw another arc cutting the previous arc at R.
  • Join HR and AR.
    Then, HEAR is the required parallelogram.

(iv) We known that the opposite sides of a rectangle are equal and each angle of it is 90°.
Make a rough sketch of the required
rectangle and write down its dimensions.

Steps of Construction :
NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry 20

  • Draw OK = 7 cm.
  • Draw ∠OKX = 90°.
  • With K as centre and radius 5 cm, draw an arc KX at A.
  • With A as centre and radius 7 cm, draw an arc.
  • With O as centre and radius 5 cm, draw another arc cutting the previous arc at Y.
  • Join AY and OY.
    Then, OKAY is the required rectangle.

Take Your IIT JEE Coaching to Next Level with Examtube

  • Mentoring & Teaching by IITians
  • Regular Testing & Analysis
  • Preparation for Various Engineering Entrance Exams
  • Support for School/Board Exams
  • 24/7 Doubts Clarification