Question

If the area of 2 similar triangle are equal.then prove that
they. are congruent

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Answer 1

Step-by-step explanation:

Given that:

ar△ABC=ar△DEF

Prove that:

△ABC≅△DEF

Proof: 

Two triangles ABC and DEF are shown in figure.

ar△ABC=ar△DEF (given)

ar△DEFar△ABC=1

$\frac{{de}^{2} }{ {ab}^{2} } = \frac{ {ef}^{2} }{ {bc}^{2} } = \frac{ {fd}^{2} }{ {ca}^{2} } = 1$

[ USING THEOREM OF AREA OF SIMILAR TRIANGLES]

AB=DE,BC=EF,CA=FD

Thus, △ABC≅△DEF                                      [BY SSS criterion of congruence]

THEOREM OF AREA OF SIMILAR TRIANGLES -

If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides. This proves that the ratio of areas of two similar triangles is proportional to the squares of the corresponding sides of both the triangles.

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