Question

if the area of two similar triangles are equal then prove that they are congurent​

Answer 1

Answer:

We cannot prove this because if two triangles are congurent then there area are equal but when area are equal we do not have any proof that they are congurent

Hope it helps you

Answer 2

Step-by-step explanation:

let us consider that the two triangles are ΔABC and ΔPQR

given they are similar ΔABC ≈ ΔPQR

hence AB/PQ = BC/QR = AC/PR (corresponding sides of similar triangles)

also as their areas are equal

ar(ΔABC) = AB² = BC² = AC²     (ratio of areas of similar triangles)

ar(ΔPQR)    PQ²    QR²    PR²

as area of the two triangles is equal their ratio will be 1

hence AB²/PQ² = 1 , BC²/QR² = 1  ,  AC²/PR² = 1

then, AB² = PQ² , BC² = QR² , AC² = PR²

taking square roots

AB = PQ, BC=QR ,AC = PR

by SSS condition

ΔABC ≅ ΔPQR

hence proved