Question

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

Answer 1

$\huge\star\underline\mathfrak\red{Answer:-}$

➡ 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.

Answer 2

$\textbf{Answer is in attachment!}$