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

  • question_answer
    In the given figure, ABC is an isosceles triangle in which\[AB=AC\]. If E and F be the midpoints of AC and AB respectively, then BE is equal to ____.

    A)  CF                             

    B)  AB                 

    C)  CE                 

    D)         BF                 

    Correct Answer: A

    Solution :

    Since, AB = AC \[\Rightarrow \]  \[\frac{1}{2}AB=\frac{1}{2}AC\] \[\Rightarrow \] \[BF=EC\] Also.  \[AB=AC\text{ }\Rightarrow \text{ }\angle B=\angle C\] [Angles opposite to equal sides are equal] In \[\Delta \text{ }BEC\]and \[\Delta \text{ }CFB\] EC = FB              (proved above) \[\angle B=\angle C~\]           (proved above) BC = BC             (common) \[\therefore \] \[\Delta \,BEC\cong \Delta \,CFB\]        (By SAS) \[\Rightarrow \] \[BE=CF\]             (By CPCT)


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