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Question

If area of ABC= area of DEF then prove that ABCDEF

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Solution

Given ABCDEF

We know that if two triangles are similar, then the ratio of there are equal to the square of the ratio of its corresponding sides.

areaABCareaDEF=(BCEF)2=(ABDE)2=(ACDF)2

areaDEFareaDEF=(BCEF)2=(ABDE)2=(ACDF)2

since areaABC=areaDEF

1=(BCEF)2=(ABDE)2=(ACDF)2

1=(BCEF)2,1=(ABDE)2,1(ACDF)2

BCEF=1,ABDE=1,ACDF=1

BC=EF,AB=DE,AC=DF

Hence by SSS congruency,

ABCDEF

Hence proved.

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