Symmetry · Usually met around P3
Completing symmetric shapes on squared paper
The same distance from the line; a square on a slanting line is its own partner.
How to do it
Method
The same distance from the line; a square on a slanting line is its own partner
Line from the top left: row 1, column 3 ↔ row 3, column 1
Another way
Imagine the fold
Fold on the dashed line: shade where each square lands
In full
Every shaded square on one side of the line of symmetry needs a partner just as far from the line on the other side. An upright line: flip left to right along the same row; a flat line: flip top to bottom in the same column. A slanting line (along the squares' diagonals): count how many steps the square is from the line and in which direction, and its partner is the same number of steps on the other side, with row and column swapped: row 1, column 3 pairs with row 3, column 1. A square the slanting line passes through is its own partner and needs nothing more. Another way: imagine folding the paper on the dashed line, or turn the paper so the slanting line looks upright, then finish it. Check: folded, every square matches, and the shape was not just copied across or turned half round.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
The dashed line is a line of symmetry. To finish the symmetric shape, how many more squares must be shaded on the other side?
Show the answer and working
Answer: 5 squares
Every shaded square needs a partner on the other side of the line: 5 squares.
Example 2
The dashed line is a line of symmetry. Folded along it, which square does ★ land on?
- A. A
- B. D
- C. C
- D. B
Choose the right answer
Show the answer and working
Answer: C. C
★'s partner is just as many steps from the line on the other side, flipped as in a mirror.
Example 3
★ is in row 1, column 1 (rows from the top, columns from the left). Folded along the slanting dashed line, ★ lands in row □, column □.
Fill in each box
Show the answer and working
Answer: 6，6
Flipped over the slanting line, ★ stays just as far from it: row 6, column 6.
Practise it in the game →Symmetry · Free to start, unlimited questions, no download