Math, asked by manish410, 1 year ago

if the area of two similar triangles are equal prove that they are congruent

Answers

Answered by laynahaycraft
16
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.________________________________________________________
Solution: 
[Fig is in the attachment]
Given: ΔABC ~ ΔPQR. & 
ar ΔABC =ar ΔPQR
To Prove: ΔABC ≅ ΔPQR
Proof: Since, ΔABC ~ ΔPQRar 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]



manish410: thanks
laynahaycraft: welcome
athivjlijaykumar: nice
Answered by athivjlijaykumar
6
ar(∆ABC)=ar(∆pqr). - 1
√ar(∆abc)\ar(pqr)=ab\pq
from both,
√1=ab\pq
1=ab\pq
ab=pq
therefore, ∆abc=~∆pqr
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