question_answer

D, BE and CF, the altitude of AABC are equal. Then

A)  AC = BC        

B)         AD = AB        

C)         AB = CF         

D)         None of these

Correct Answer: A

Solution :

In right triangles BCE and CBF. BC = CB                                  [Common] BE = CF                                   [Given] \[\angle BEC=\angle CFB\]                                  [Each \[{{90}^{o}}\]] \[\therefore \]\[\Delta BCE=\Delta CBF\]    [By R.H.S congruency] \[\Rightarrow \]\[\angle CBE=\angle BCF\]             [By C.P.C.T.] and \[\angle ABC=\angle ACB\] \[\Rightarrow \] AC = AB                               [Sides opposite] To equal angles of a \[\Delta \] are equal similarity, \[\Delta \Alpha \Beta D\cong \Delta BAE\] \[\Rightarrow \]\[\angle ABC=\angle BAC\]             [By C.P.C.T.] \[\Rightarrow \]AC = BC [Sides opposite to equal angles of a \[\Delta \]are equal]