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7th Class Mathematics Congruence of Triangles Question Bank Congruence of Triangles

  • question_answer
    Akira gave a problem to her sister Kiara. However, Kiara got stuck. Help Kiara identify whether the triangles are congruent and choose the correct option.

    A)  Yes, \[\Delta ABC\cong \Delta DCE\]

    B)  No, they are not congruent        

    C)  Yes. \[\Delta DCE\cong \Delta CAB\]

    D)  Yes, \[\Delta DEC\cong \Delta CAB\]

    Correct Answer: D

    Solution :

    In the given figure,          \[MD=MC=EC=EB=AB\] \[\Rightarrow \]\[DC=MD+MC=CE+EB=CB\]...(1) Also, \[AB=EC\]                     ...(2) In \[\Delta DEC\]and \[\Delta CAB\] \[DE=CA\]                         (given) \[DC=CB\]      (from(1)) \[EC=AB\]      (from (2)) \[\therefore \]  \[\Delta DEC\cong \Delta CAB\](By SSS)


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