Mathematics
State whether the following statement is true or false. Justify your answer:
"A straight line dividing a figure into two identical parts is necessarily a line of symmetry."
Symmetry
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Answer
False.
Justification — A line of symmetry must divide a figure into two coincident parts that are mirror images of each other. Two parts of a figure may be identical (congruent — same shape and size) without being mirror images of each other.
For example, the diagonal of a parallelogram divides it into two congruent (identical) triangles, but if we fold the parallelogram along this diagonal, the two triangles do not coincide. So the diagonal is not a line of symmetry of the parallelogram.
∴ A straight line dividing a figure into two identical parts is not necessarily a line of symmetry.
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