Question

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

Answer 1

Answer:

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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