Class 10th -Triangle - chapter 6- Exercise 6.2 sum no.1 and sum no 2

 Exercise 6.2

Question 1:-

 

Solution:-

In Figure (i) and (ii) DE || BC., Find EC in (i) and AD in (iii)

(i)  Let EC= x cm

 Given :- DE || BC, therefore using Thales Theorem, we have

AD/DB = AC/EC

➱1.5/3=1/x 

➱ x=(3*1)/1.5 =2

Hence, EC=2.

(ii)            Let AD= x cm

 Given :- DE || BC, therefore

using Thales Theorem, we have

AD/DB= AC/EC

➱x / 7.2=1.8 / 5.4

➱x=(1.8 * 7.2) / 5.4=2.4

Hence, AD=2.4

 

 

Question:-2  

E and F are points on the sides PQ and PR respectively of a ΔPQR. For each of the following cases, state whether EF || QR. 

(i) PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm (ii) PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm (iii)PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.36 cm

Solution:-


(i)
(i)  PE/EQ= 3.9/3=1.3
and PF/FR= 3.6/2.4= 3/2=1.5
since, PE/EQ≠PF/FR
 EF∦QR

(ii)
  
(ii)
 PE/EQ=4/4.5
                 =40/45=8/9
and,     PF/FR= 8/9
since, PE/EQ=PF/FR
 EF∥QR
(iii)

(iii)
In△PQR, PQ=1.28 and PE=0.18
so EQ= PQ-PE=1.28-0.18=1.10
 and, PR=2.56 and PF=0.36
so, FR=PR-PF=2.56-0.36=2.20
       PE/EQ=0.18/1.10=9/55
and PF/FR=0.36/2.20=9/55
since, PE/EQ=PF/FR
        EF∥QR
 


  

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