If a rectangle has more than two lines of symmetry, then it must be a square.
Answer: True
Step 1: A line of symmetry is a line that cuts a shape into two matching halves (mirror images).
Step 2: In any rectangle, opposite sides are equal and all angles are right angles.
Step 3: Every rectangle has exactly two “middle” symmetry lines:
Step 4: What about the diagonals?
For a general rectangle, the two diagonals are not lines of symmetry because they would try to swap the long side with the short side.
( ext{Let length} = l )
( ext{Let breadth} = b )
( ext{In a general rectangle: } l e b )
If a diagonal were a symmetry line, swapping across it would require the two adjacent sides to match exactly.
( ext{For diagonal symmetry we need } l = b )
Step 5: The condition ( l = b ) means all sides are equal — that turns the rectangle into a square.
( l = b Rightarrow ext{rectangle with equal sides} Rightarrow ext{square} )
Step 6 (Conclusion): A rectangle already has 2 symmetry lines. If it has more than two, the extra ones are the diagonals — and that happens only when ( l = b ), i.e., the rectangle is a square. Therefore, the statement is true.
Quick check: A square has 4 lines of symmetry — vertical, horizontal, and the two diagonals.