Advertisements
Advertisements
प्रश्न
If the areas of two similar triangles are equal, prove that they are congruent.
बेरीज
Advertisements
उत्तर
Let us assume two similar triangles as ΔABC ~ ΔPQR
`(ar(triangleABC))/(ar(trianglePQR)) = ((AB)/(PQ))^2 = ((BC)/(QR))^2 = ((AC)/(PR))^2` ...(1)
Given that, ar(ΔABC) = ar(ΔABC)
`=> (ar(triangleABC))/(ar(trianglePQR)) = 1`
Putting this value in equation (1), we obtain:
`1 = ((AB)/(PQ))^2 = ((BC)/(QR))^2 = ((AC)/(PR))^2`
⇒ AB = PQ, BC = QR and AC = PR
∴ ΔABC ≅ ΔPQR (By SSS congruence criterion)
shaalaa.com
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
