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]You need to login to perform this action.
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