1.

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

Answer»

Answer:

Step-by-step EXPLANATION:

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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