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9th Class Mathematics Triangles Question Bank Triangles

  • question_answer
    If AD is bisector of \[\angle A\]and D is perpendicular to BC. Then AABC is ___ triangle.

    A)  Isosceles                 

    B)         Equilateral                   

    C)         Scalene                       

    D)         None of these       

    Correct Answer: A

    Solution :

    In \[\Delta ADB\]and\[\Delta ADC\] \[\angle BAD=\angle CAD\]                     (\[\because \]AD bisects \[\angle A\]) \[\angle ADB=\angle ADC\]                     (\[\because \] Each\[{{90}^{o}}\]) AD = AD                      (common) \[\Delta ADB\cong \Delta ADC\]                (ASA congruency) \[\therefore \]AB = AC                (by (PCT)) \[\therefore \]\[\Delta ABC\]is an isosceles triangle.


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