MathematicsState whether the following statement is true or false.If ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see figure), then ∆ABE ≅ ∆ACF. 

State whether the following statement is true or false.
If ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see figure), then ∆ABE
 ∆ACF.


 

  1. A
    True
  2. B
    False 

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    Solution:

    Given that ∆ABC is a triangle, where BE & CF are altitudes to the respective sides AC and AB such that BE=CF.
    Consider AEB=AFC                            [From eq (1)]  
    A=A                                       [Common]  
    BE=CF                                             [Given]  
    Thus, by AAS congruence criteria,

    Hence, by AAS congruence criteria, we proved thatTherefore, the given statement is true.
    So, option (1) is correct.
     
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