Question

Which congruence criterion do you use in the following?
Given: EB$=$BD, AE$=$CB, $\angle$A$=\angle$C$={90}^o$. So $\Delta$ABE$\equiv \Delta$CDB.

Answer 1

By RHS congruence criterion,

since it is given that

EB$=$BD, AE$=$CB, $\angle$A$=\angle$C$={90}^o$
Hypotenuse and one side of a right angled triangle

are respectively equal to the hypotenuse and one side

of another right angled triangle.
Therefore,

$\Delta$ABE$\cong \Delta$CDB.