If the areas of two similar triangle are equal,show that they are congruent.
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Answer:
Step-by-step explanation:
Use the theorem that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides , then prove that they are congruent.
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Solution:
[Fig is in the attachment]
Given: ΔABC ~ ΔPQR. &
ar ΔABC =ar ΔPQR
To Prove: ΔABC ≅ ΔPQR
Proof: Since, ΔABC ~ ΔPQR
ar ΔABC =ar ΔPQR. (given)
ΔABC / ar ΔPQR = 1
⇒ AB²/PQ² = BC²/QR² = CA²/PR² = 1
[ USING THEOREM OF AREA OF SIMILAR TRIANGLES]
⇒ AB= PQ , BC= QR & CA= PR
Thus, ΔABC ≅ ΔPQR
[BY SSS criterion of congruence]
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