Chapter 4. Practical Geometry

Exercise 4.1

1. Construct the following quadrilaterals.
(i) Quadrilateral ABCD.      
AB = 4.5 cm                                    
BC = 5.5 cm                                  
CD = 4 cm                                      
AD = 6 cm                                      
AC = 7 cm                                      

(ii) Quadrilateral JUMP
   JU = 3.5 cm
  UM = 4 cm
  MP = 5 cm

   PJ = 4.5 cm
  PU = 6.5 cm

(iii) Parallelogram MORE       
OR = 6 cm                                         
RE = 4.5 cm                                        
EO = 7.5 cm

(iv) Rhombus BEST

BE = 4.5 cm

ET = 6 cm

Exercise 4.2

1. Construct the following quadrilaterals.
(i) quadrilateral LIFT         (ii) Quadrilateral GOLD
LI = 4 cm                                    OL = 7.5 cm
IF = 3 cm                                    GL = 6 cm
TL = 2.5 cm                                GD = 6 cm
LF = 4.5 cm                                LD = 5 cm
IT = 4 cm                                    OD = 10 cm
(iii) Rhombus BEND
BN = 5.6 cm
DE = 6.5 cm

Exercise 4.3

1. Construct the following quadrilaterals.
(i) Quadrilateral MORE    (ii) Quadrilateral PLAN
MO = 6 cm                                 PL = 4 cm
OR = 4.5 cm                               LA = 6.5 cm
∠M = 60°                                    ∠P = 90°
∠O = 105°                                  ∠A = 110°
∠R = 105°                                   ∠N = 85°
(iii) Parallelogram HEAR        (iv) Rectangle OKAY
HE = 5 cm                                   OK = 7 cm
EA = 6 cm                                   KA = 5 cm
∠R = 85°

Exercise 4.4

1. Construct the following quadrilaterals.
(i) Quadrilateral DEAR        (ii) Quadrilateral TRUE
          DE = 4 cm                                  TR = 3.5 cm
          EA = 5 cm                         RU = 3 cm
          AR = 4.5 cm                      UE = 4 cm
           ∠E = 60°                          ∠R = 75°
           ∠A = 90°                         ∠U = 120°

Exercise 4.5

Draw the following.
1. The square READ with RE = 5.1 cm.
2. A rhombus whose diagonals are 5.2 cm and 6.4 cm long.
3. A rectangle with adjacent sides of lengths 5 cm and 4 cm.
4. A parallelogram OKAY where OK = 5.5 cm and KA = 4.2 cm. Is it unique?