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9th Class Mathematics Triangles Question Bank Triangles

  • question_answer
    In the given figure, \[AD\] is the bisector of \[\angle A\] and\[AB=AC\]. By which criterion are \[\Delta ABD\] and \[\Delta ACD\]congruent? (i)  S.S.S.                      (ii) S.A.S.                      (iii) A.SA                       (iv) R.H.S.                    

    A)  (i) only            

    B)         (ii), (iii) and (iv) only                  

    C)         (i) and (iii)                    

    D)         (ii) and (iv) only

    Correct Answer: B

    Solution :

    In \[\Delta ABC,AB=AC\Rightarrow \angle B=\angle C\] \[AB=BC\Rightarrow \angle B=\angle C\] \[AD\bot BC\Rightarrow BD=DC\] In \[\Delta \Alpha \Beta D\]and \[\Delta \Alpha CD,\] \[AB=AC\](side) AD is the common side \[\angle DAB=\angle DAC\] (Since AD bisects\[\angle A.\]) \[\therefore \,\Delta ABD\cong \Delta ACD\](By A.S.A criterion)


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