Question

State whether the following statemnt is true or false.
If two triangles are equal in perimeter, they must be congruent.

Answer 1

$\underset{–}{\text{Congruent Triangles}}$ :
Two triangles are said to be congruent if they are of the same shape and size.

$\underset{–}{\text{Given}}$ : Two triangles are equal in perimeter.
Perimeter of $△ABC=3+4+5=12$
Perimeter of $△PQR=4+4+4=12$
But, clearly they don't have the same shape.
Thus, they are not congruent.

Hence, the given statement is $\text{false}$.