Question

if area of two triangles are equal prove that they are congruent

Answer 1

given traingle ABC is congruent to triangle PQR
we know that if triangles are similar
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

Answer 2

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 by SSS congruence