if the areas of two similar triangles are equal,show that triangles are congruent
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Consider two triangles viz., ΔABC and ΔDEF which are similar to each other.
Given, Area of ΔABC = Area of ΔDEF
Now, we know that ratio of area of two similar triangle is equal to the ratio of squares of their corresponding sides.

∴ All the sides of ΔABC are equal to the corresponding sides of ΔDEF.
 [SSS property]
Given, Area of ΔABC = Area of ΔDEF
Now, we know that ratio of area of two similar triangle is equal to the ratio of squares of their corresponding sides.

∴ All the sides of ΔABC are equal to the corresponding sides of ΔDEF.
 [SSS property]
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