If the area of two similar triangles are equal, prove that they are congruent.
Given that:
ar△ABC=ar△DEF
Prove that:
△ABC≅△DEF
Proof:
Two triangles ABC and DEF are shown in figure.
ar△ABC=ar△DEF (given)
ar△ABCar△DEF=1
AB2DE2=BC2EF2=CA2FD2=1 [ USING THEOREM OF AREA OF SIMILAR TRIANGLES]
AB=DE,BC=EF,CA=FD
Thus, △ABC≅△DEF [BY SSS criterion of congruence]