if the area of two similar triangles are equal then prove that they are congruent
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Given:- Let ∆ABC ~ ∆DEF [given]
ar(∆ABC) = ar(∆DEF)
To Prove:- ∆ABC congruent to ∆DEF.
Proof:- Since ∆ABC ~∆DEF
LA = LD, LB = LE and LC = LF
AB/DE = BC/EF = AC/DF________eq.(i)
Since ar(∆ABC) = ar(∆DEF)
ar(∆ABC)
_______ = 1.
ar(∆DEF)
(AB/DF)² – (BC/EF)² = (AC/DF)²
(AB/DF)² = 1²
AB/DF = 1
AB = DF.
Similarly, BC = EF and AC = DF _______eq.(ii)
From equation (i) & (ii), we get:
∆ABC congruent to ∆DEF.
Hence Proved.
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