Lesson Guide
Explanation
A line of symmetry is a fold line: fold along it and the two halves land exactly on each other. A rectangle folds across and down, two lines — but not along its diagonals, because the corners miss. A square folds four ways, adding both diagonals. An isosceles triangle folds one way only. And some shapes that look balanced have none at all: a leaning parallelogram, or a scalene triangle. Test every line you can think of, then count.
Your Turn
How many lines of symmetry does a kite have? Check: 1, down its long diagonal.
Watch Out
A rectangle does NOT fold along its diagonals. Only a square among the rectangles does.
Explanation
A regular shape — all sides equal and all angles equal — has one line of symmetry for every side. A regular pentagon has five, a regular hexagon six, a regular octagon eight, and the square is the regular quadrilateral with four. When the number of sides is odd, each line runs from a corner to the middle of the opposite side. The rule only holds for regular shapes, so check that word in the question: an irregular hexagon might have one line, two, or none at all.
Your Turn
How many lines of symmetry does a regular octagon have? Check: 8.
Watch Out
The rule needs the word "regular". An irregular pentagon does not have five lines.
Explanation
Digits have symmetry too. Written plainly, zero, one, three and eight fold across the middle, while only zero, one and eight fold down the middle. So eighty-eight folds both ways, three folds across only, and two, five, six, seven and nine fold neither. The largest two-digit number with a line of symmetry across the middle is eighty-eight. Letters work the same way — A, M, T, U, V, W and Y fold down the middle, H, I, O and X fold both ways — and down and across are different questions, so read which one is asked.
Your Turn
Which digits fold down the middle? Check: 0, 1 and 8.
Watch Out
"Across the middle" and "down the middle" give different answers. 3 folds across but not down.
Explanation
To finish a symmetrical pattern, work outwards from the fold line. The tile beside it must match the tile on the other side, then the next pair, then the next. Counting from the ends says the same thing: the first square partners the last, the second partners the second-last. Three coloured tiles on the left of a six-square row need three more, mirrored. And when the row has an odd number of squares, the middle one sits on the fold and has no partner at all.
Your Turn
A row of 7 squares is symmetrical. Which position partners position 2? Check: position 6.
Watch Out
Mirror outwards, do not repeat. The pattern reverses after the fold rather than starting again.
Explanation
The word exactly does most of the work in these questions. A square does have two lines of symmetry — and two more besides, so it is the wrong answer to exactly two. Count every line a shape has, then compare that total with the number the question asks for. The rest is the fold test, the regular-shape rule, and working outwards from the fold. Quiz and exercises now.
Your Turn
Does a square answer "which shape has exactly two lines of symmetry"? Check: no — it has four.
Watch Out
Find ALL the lines before choosing. Stopping as soon as you find two picks the square.
📌 Key Points — this lesson in a nutshell
- A line of symmetry is a fold line: the two halves land exactly on each other.
- A regular shape has as many lines as it has sides — a square 4, a regular pentagon 5, a regular hexagon 6.
- "Exactly two" rules out a shape with four. Count them all before you answer.
- To finish a symmetrical pattern, work outwards from the fold: each tile must match its partner the same distance away.
Step 1: Introduction
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