Question

If the area of two similar triangles are equal prove that they are congruent

Answer 1

Let triangles ABC and PQR have equal areas. 

we have the formula for area of similar triangles.

 area of ABC/area of PQR= AB2/PQ2 = BC2/QR2= AC2/PR2

 but given that

ar(ABC)=ar(PQR) 

implies that

AB=PQ, BC=QR, AC=PR. 

therefore

triangle ABC≅ triangle PQR