Question

If the areas of two similar triangles are equal 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△DEF

ar△ABC

=1

DE

2

AB

2

=

EF

2

BC

2

=

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]