D0 — the sides are equal, so no one line divides it differently
A square has 4 lines of symmetry: the vertical midline, the horizontal midline, and both diagonals. All four fold the square so both halves align perfectly. A non-square rectangle only has 2 (the two midlines) because its diagonals fold to triangles whose long and short sides don't match.
Question 2 Multiple Choice
A student draws a diagonal on a non-square rectangle and says it is a line of symmetry because it 'divides the rectangle into two equal triangles.' What is the error in this reasoning?
AA rectangle cannot be divided along a diagonal
BDividing into two pieces of equal area is not the same as a line of symmetry — the two triangles don't match when folded
COnly horizontal lines can be lines of symmetry for rectangles
DNon-square rectangles have no lines of symmetry at all
A line of symmetry requires the two halves to be mirror images that align exactly when folded. Folding a non-square rectangle along a diagonal produces two triangles that don't align: the long side of one overhang the short side of the other. Dividing in half by area is a weaker condition than symmetry — the rectangle has exactly 2 lines of symmetry, both midlines.
Question 3 True / False
A shape can be divided into two halves of equal area without having a line of symmetry.
TTrue
FFalse
Answer: True
True. Many lines can split a shape into equal areas without either half being a mirror image of the other. The diagonal of a non-square rectangle cuts it into two equal-area triangles, but they don't fold to match — corners land in wrong positions. Line symmetry requires mirror-image matching, not just equal areas.
Question 4 True / False
A regular pentagon has exactly 5 lines of symmetry.
TTrue
FFalse
Answer: True
True. A regular polygon with n sides has exactly n lines of symmetry. A regular pentagon has 5 sides, so it has 5 lines of symmetry — one through each vertex and the midpoint of the opposite side. This pattern holds for all regular polygons.
Question 5 Short Answer
What does it mean for a line to be a 'line of symmetry'? Why does the vertical midline of a rectangle qualify, but its diagonal does not?
Think about your answer, then reveal below.
Model answer: A line of symmetry divides a figure into two halves that are exact mirror images — when folded along that line, both halves align perfectly with no part sticking out. The vertical midline of a rectangle works because folding places the left half exactly over the right half. The diagonal doesn't work because the corners and sides land in wrong positions — the two triangles formed are congruent but do not fold onto each other.
The test for a line of symmetry is folding, not measuring area. 'Equal halves' by area is a weaker condition than mirror-image symmetry. For true symmetry, every point on one side must have a matching point at the same distance on the other side — and that only happens with the rectangle's midlines.