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Question
(i) In Fig. 7.70, if AB ||CD, find the value of x.
(ii) In Fig. 7.71, if AB || CD, find the values of x.
(iii) In Fig. 7.72 AB||CD, If OA =3x-19, OB=x-4, OC=x-3 and OD= 4, find x.
(i) In Fig. 7.70, if AB ||CD, find the value of x.
(ii) In Fig. 7.71, if AB || CD, find the values of x.
(iii) In Fig. 7.72 AB||CD, If OA =3x-19, OB=x-4, OC=x-3 and OD= 4, find x.
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Solution
In 
ABO and 
DCO
AOB = 
DOC (vertically opposite angles)
BAO = 
DCO (alternate interior angles ) (AB ||CD)
ABO = 
CDO (alternate interior angles ) (AB ||CD)
Hence 
ABO and 
DCO are similar by AAA.
Therefore,
( corresponding parts of similar triangles)
(i)
x=2 and x=3 satisfy all the equations and none of the sides becomes negative. Hence x = 2 or 3
(ii)
x = 
and 2 satisfy all the equations and none of the sides becomes negative. Hence x = 
or 2.
(iii)
x cannot be 3.3 because then x-4 will be negative and a side can never be negative.
Hencc x = 7.36
ABO and DCOAOB = DOC (vertically opposite angles)BAO = DCO (alternate interior angles ) (AB ||CD)ABO = CDO (alternate interior angles ) (AB ||CD)Hence
ABO and DCO are similar by AAA.Therefore,
( corresponding parts of similar triangles)(i)
x=2 and x=3 satisfy all the equations and none of the sides becomes negative. Hence x = 2 or 3
(ii)
x =
and 2 satisfy all the equations and none of the sides becomes negative. Hence x = or 2.(iii)
x cannot be 3.3 because then x-4 will be negative and a side can never be negative.
Hencc x = 7.36
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