Areas of two Similar traingals are Equal, Prove that they are Congruent | Bzziii.com

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If the areas of two similar traingals are equal, Prove that they are congruent.







Given,

ar (`\triangle`ABC) = ar (`\triangle`PQR)

`\triangle`ABC 〜 `\triangle`DEF

We Know that

`\frac{\triangle "ABC"}{\triangle "PQR"}` = `"AB"^2/"PQ"^2` = `"BC"^2/"QR"^2` = `"CA"^2/"PR"^2`

Now,

1 = `"AB"^2/"PQ"^2`

AB = PQ


Similarly,

1 = `"BC"^2/"QR"^2`

BC = QR

and,

1 = `"CA"^2/"PR"^2`

CA = PR

Thus, AB = PQ, BC = QR and CA = PR

∴ `\triangle "ABC" \cong \triangle "PQR"`



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