Question

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

Answer 1

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Answer 2

Given = two triangles ABC and DEF such that triangle ABC is similar to
Triangle DEF.
To prove = triangle ABC is congruent to triangle DEF.
Proof= we have
Triangle ABC is similar to triangle Triangle DEF. Such that
AngleA = angle D
Angle B = angle E
Angle C = Angle F
AB/ DE = BC/EF= AC/ DF
IN order to prove Triangle abc is congruent to triangle def it is sufficient to prove that AB= DE, BC = EF, AC= DF.
IT IS GIVEN THAT
AREA ( triangle abc) = AREA( triangle def)
AREA ( triangle abc) / Area ( triangle def )= 1
AB² / DE² = BC²/ EF² = AC²/ DF²
AB² =DE² , BC²= EF² , AC² = DF²
AB= DE, BC = EF, AC= DF
THEREFORE,
TRIANGLE ABC IS CONGRUENT TO TRIANGLE DEF.
hope it helps......