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Q.

State true or false.


In the given figure, ABC  is a triangle in which AB=AC   and D   is a point on AB  . Through D  , a line DE   is drawn parallel to BC   and meeting AC   at E  . Then AD≠AE  .


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a

True

b

False 

answer is B.

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Detailed Solution

It is given that AB=AC   .
D   is a point on AB  .
DE   is drawn parallel to BC   and meeting AC   at E  .
Question ImageFrom the above figure,
AB=AC   and DE∥BC  .
By basic proportionality theorem,
AD DB = AE EC   and
DB AD = EC AE                               ……(1)
Analyze equation (1) and add 1 on both sides.
DB AD +1= EC AE +1  
By simplification,
DE+AD AD = EC+AE AE  
AB AD = AC AE  
But AB=AC  ,
AB AD = AC AE  
AD=AE  
But the statement given is AD≠AE  .
Hence the given statement is false.
Hence the correct statement is for a triangle ABC, when a line DE is parallel to BC and meeting AC at E, thn AD = AE.
Therefore option 2 is correct.
 
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State true or false.In the given figure, ABC  is a triangle in which AB=AC   and D   is a point on AB  . Through D  , a line DE   is drawn parallel to BC   and meeting AC   at E  . Then AD≠AE  .