Question

State whether the following statement is true or false:
If two triangles are equal in area, 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 area.

For example, These two triangles have the same base and height, i.e. they are equal in area.

But, they don't have the same shape.
Thus, they are not congruent.

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