Question

if area of two triangle are similar and equal prove that they are congrent

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