Lines and Symmetry — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
A square has exactly 2 lines of symmetry.
Corrected: A square has exactly 4 lines of symmetry: 2 diagonal and 2 through the midpoints of opposite sides.
The corrected sentence is: "A square has exactly 4 lines of symmetry: 2 diagonal and 2 through the midpoints of opposite sides.". The original sentence "A square has exactly 2 lines of symmetry." contained an error that needed to be fixed.
2. Fix the sentence:
A circle has only 1 line of symmetry through its center.
Corrected: A circle has infinitely many lines of symmetry because any line through the center divides it into equal halves.
The corrected sentence is: "A circle has infinitely many lines of symmetry because any line through the center divides it into equal halves.". The original sentence "A circle has only 1 line of symmetry through its center." contained an error that needed to be fixed.
3. Fix the sentence:
A rectangle always has 4 lines of symmetry just like a square.
Corrected: A rectangle has 2 lines of symmetry through the midpoints of opposite sides. Its diagonals are not lines of symmetry.
The corrected sentence is: "A rectangle has 2 lines of symmetry through the midpoints of opposite sides. Its diagonals are not lines of symmetry.". The original sentence "A rectangle always has 4 lines of symmetry just like a square." contained an error that needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. A line of symmetry divides a shape into two equal halves.
A line of symmetry splits a shape so each half is a mirror image of the other — they are congruent (equal).
2. An equilateral triangle has 3 lines of symmetry.
An equilateral triangle has 3 equal sides and 3 lines of symmetry — one through each vertex and the midpoint of the opposite side.
3. A regular pentagon has 5 lines of symmetry.
A regular polygon's lines of symmetry equal its number of sides. A regular pentagon has 5 sides → 5 lines of symmetry.
4. A shape with no line of symmetry is called asymmetric.
An asymmetric (or asymmetrical) shape cannot be folded along any line to produce two matching halves.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. How can you test whether a line is a line of symmetry?
Sample answer: Fold the shape along the line. If both halves match exactly, the line is a line of symmetry.
The fold test is the standard method: if both halves overlap perfectly, the fold line is a line of symmetry.
2. Why does a rectangle have fewer lines of symmetry than a square?
Sample answer: A rectangle has unequal side lengths, so its diagonals do not create matching halves, while a square has equal sides so all four possible fold lines work.
A rectangle has 2 lines of symmetry (horizontal and vertical only); a square has 4 (horizontal, vertical, and both diagonals) because all sides are equal.