The perimeter of one triangle is equal to the perimeter of the other. Can these triangles be equal?

| August 5, 2021 | education

Two triangles can be equal if they can be overlapped. That is, two triangles will be equal if the elements, namely the angles and sides, of the triangle are respectively equal to the elements of the other triangle.

The perimeter of a triangle is the sum of the lengths of all its sides.

For example, consider two triangles ABC and EDF. Perimeter PABC = AB + BC + AC, and perimeter

PEDF = ED + DF + EF.

Since the task says that the perimeter of one triangle is equal to the perimeter of the other, then PABC = PEDF. Therefore, the sides of these triangles will also be equal to each other. And since the three sides of one triangle are respectively equal to the three sides of the other triangle, then such triangles are equal.

Answer: two triangles can be equal if the perimeter of one triangle is equal to the perimeter of the other.



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