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7th Class Mental Ability Geometry Question Bank Geometry

  • question_answer
    In a triangle ABC, BD and CE are perpendicular on AC and AB respectively, If BD = CE, then the triangle ABC is:

    A) Equilateral        

    B) Isosceles   

    C)    Right angled                  

    D) Scalene

    E) None of these

    Correct Answer: B

    Solution :

    Explanation In ABDC and ABEC, \[\operatorname{BC} = BC\]         (common) \[\angle BDC=\angle BEC\]   (each equal to 90°) \[\operatorname{BD}=CE\]    (Given) \[\therefore \,\,\,\Delta BDC\cong \Delta BEC\] \[\angle DCB\,\,=\,\,\angle EBC\]       (By c.p.c.t) \[\Rightarrow \,\,\,\, AB = AC\]  (Sides opposite to equal adjacent angles in a triangle) Hence, the \[\Delta ABC\] is an isosceles triangle.


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