How many lines of symmetry does a rectangle (that is not a square) have?
A4, the same as a square
B0, because rectangles have no symmetry
C2, through the midpoints of opposite sides only
D2, along both diagonals
A rectangle has exactly 2 lines of symmetry: one connecting the midpoints of the top and bottom sides, and one connecting the midpoints of the left and right sides. The diagonals are NOT lines of symmetry — when you fold a rectangle along a diagonal, the two triangular halves do not align (the corners don't match up). A square has 4 lines of symmetry because its equal side lengths allow the diagonal folds to work; a rectangle's unequal sides prevent this.
Question 2 Multiple Choice
A student draws a diagonal line from corner to corner across a rectangle and claims it is a line of symmetry. Why is the student wrong?
ARectangles cannot have any lines of symmetry at all
BWhen folded along the diagonal, the two triangular halves do not align — the shorter and longer sides swap positions, so corners don't stack
CLines of symmetry must always be vertical or horizontal
DThe diagonal creates two triangles, and triangles are not allowed in symmetry problems
The test for a line of symmetry is folding: both halves must stack exactly. When you fold a non-square rectangle along a diagonal, you get two right triangles — but the short side of one lands on the long side of the other. They don't match. This is the key difference between a rectangle and a square: a square's equal sides mean the diagonal fold works, giving it 4 lines of symmetry. For a rectangle, only the horizontal and vertical midpoint lines pass the fold test.
Question 3 True / False
A line of symmetry divides a shape into two halves that, when folded along that line, land exactly on top of each other.
TTrue
FFalse
Answer: True
True — this is the definition of a line of symmetry. Every point on one side of the line has a mirror-image point at the exact same distance on the other side. The fold test is what makes this concrete: if any part of one half sticks out past the other, the fold line is not a true line of symmetry. Both halves must be exactly the same shape and size.
Question 4 True / False
A square and a rectangle generally have the same number of lines of symmetry.
TTrue
FFalse
Answer: False
False. A square has 4 lines of symmetry (2 through midpoints of opposite sides, plus 2 diagonals), while a rectangle that is not a square has only 2 (through midpoints of opposite sides). The diagonals of a rectangle fail the fold test because the unequal side lengths prevent the corners from aligning. Equal side lengths are what allow the diagonals to work as lines of symmetry in a square.
Question 5 Short Answer
Explain why the fold test is the most reliable way to check whether a proposed line is truly a line of symmetry.
Think about your answer, then reveal below.
Model answer: The fold test directly checks the definition: fold the shape along the proposed line and see if both halves align perfectly. If any edges, corners, or parts of one half extend beyond the other, the line is not a line of symmetry. It replaces guessing based on appearance with a physical test that reveals whether every point on one side truly mirrors the other side.
Visual inspection can be misleading — a line can look like it divides a shape evenly without actually being a line of symmetry. The fold test (or placing a mirror along the line) forces a precise check: does every part of half A land on the corresponding part of half B? This is especially important for diagonal lines on rectangles, which look plausible but fail the test. Relying on 'it looks balanced' leads to the common error of claiming rectangles have 4 lines of symmetry.