if the area of two similarity triangles are equal, prove that they are congruent
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Step-by-step explanation:
Given :-
→ ∆ABC ~ ∆DEF such that ar(∆ABC) = ar( ∆DEF) .
➡ To prove :-
→ ∆ABC ≅ ∆DEF .
➡ Proof :-
→ ∆ABC ~ ∆DEF . ( Given ) .
Now, ar(∆ABC) = ar( ∆DEF ) [ given ] .
▶ From equation (1) and (2), we get
⇒ AB² = DE² , AC² = DF² , and BC² = EF² .
[ Taking square root both sides, we get ] .
⇒ AB = DE , AC = DF and BC = EF .
[ by SSS-congruency ] .
Hence, it is proved.
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