A design has a vertical line down the middle. The left side shows a star, a circle, and a triangle from top to bottom. If the design is symmetric, what does the right side show from top to bottom?
ATriangle, circle, star — reversed order
BStar, circle, triangle — the same shapes in the same order
CStar, star, star — repeating the first shape
DCircle, triangle, star — a different arrangement
Line symmetry means the right side mirrors the left side. When you flip across a vertical line, the shapes stay at the same height — the shape at the top stays at the top, the middle stays in the middle. So the right side shows star, circle, triangle — the same shapes in the same vertical positions. The order from top to bottom does not reverse; the left-right positions mirror.
Question 2 Multiple Choice
A square has line symmetry. How many lines of symmetry does it have?
A1 — through the middle
B2 — horizontal and vertical
C4 — horizontal, vertical, and two diagonals
D0 — squares do not have symmetry
A square has four lines of symmetry: one horizontal through the middle, one vertical through the middle, and two diagonal (corner to corner). Each line divides the square into two halves that are mirror images. This makes the square one of the most symmetric common shapes — and is part of why squares appear so often in designs and patterns.
Question 3 True / False
A repeating pattern like ABABAB has symmetry.
TTrue
FFalse
Answer: True
A repeating pattern has translational symmetry — if you slide it by the length of one repeating unit (AB), it looks exactly the same. This is a different kind of symmetry from mirror symmetry, but it is genuine symmetry: a transformation (sliding) that leaves the pattern unchanged. In fact, translational symmetry is the defining feature of repeating patterns.
Question 4 Short Answer
What does it mean to say a pattern is 'symmetric,' and why is symmetry more than just a visual property?
Think about your answer, then reveal below.
Model answer: A pattern is symmetric if there is a transformation (flipping, turning, or sliding) that leaves it looking exactly the same. Symmetry is more than visual because it reveals structure: it tells you that parts of the pattern are related by a rule. If a design has mirror symmetry, knowing the left half tells you exactly what the right half looks like — the symmetry constrains the pattern. This makes symmetry a logical property: it reduces the information needed to describe the pattern and creates predictable relationships between its parts.
Symmetry as a constraint is a deep idea. In physics, symmetry principles constrain the laws of nature. In mathematics, symmetric structures have special properties. At this level, students are encountering the same core idea in a concrete form: symmetry means parts of a pattern are not independent — they are determined by each other.