Question

If triangle ABC~triangle PQR and area of triangle ABC = area of triangle PQR, then prove that triangle ABC is congruent to triangle PQR.

Answer 1

Given:ΔABC~ΔPQR
Ar(ABC)=Ar(PQR)
To prove :ΔABC is congruent to ΔPQR
Proof :ΔABC~ΔPQR(given)
Ar(ABC)/Ar(PQR)=AB²/PQ²=BC²/QR²=AC²/PR²
Ar(ABC)/Ar(ABC)=AB²/PQ²=BC²/QR²=AC²/PR²
1=AB²/PQ²=BC²/QR²=AC²/PR²
1=AB²/PQ², 1=BC²/QR², 1=AC²/PR²
AB²=PQ², BC²=QR², AC²=PR²
AB=PQ, BC=QR,AC=PR
Now in ΔABC and ΔPQR
AB=PQ
BC=QR
AC=PR
so by SSS congruency ΔABC is congruent to ΔPQR
Hence, proved

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Answer 2

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