MathematicsThe base BC of is produced on both sides of it upto points D and E. If ∠ABD   is greater than ∠ACE  , then which of the following is not true?

The base BC of is produced on both sides of it upto points D and E. If ABD   is greater than ACE  , then which of the following is not true?


  1. A
    ABC   is smaller than ACB  .
  2. B
    AC is greater than AB.
  3. C
    AB is greater than AC.
  4. D
    AB+AC>BC   

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    Solution:

    In option 1, we have ABD>ACE  . It is true. So,
    ( 180 ABD)<( 180 ACE) ABC<ACB  
    We are aware that if two angles of a triangle are equal, then its two opposite sides will also be equal. Similarly, we can apply this idea here. We already know that angle ABC is less than angle ACB.
    Consequently, side AC is less than side AB. So side AC is less than side AB.
    Consequently, the statement in option 2 contradicts this condition.
    So the correct option is 2.
     
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