Transformations: Line Symmetry

Methods in this video

Tap a time to jump to where the video teaches that method.

1. 1

   Find the partner: other side, same distance

   ▶ 0:58

   When to use it: The picture already shows one dashed line (a line of symmetry: upright, across or diagonal) and asks for the fewest extra squares to colour so that it is a line of symmetry, or what the completed pattern looks like; or a grid of paper is folded once along a line and the question asks which squares meet, or how many squares change colour.

   • A line of symmetry is a mirror: every square's partner is on the other side, the same distance away.
   • Check both sides for partners; squares that already pair up need nothing.
   • A fold flips the paper over, it doesn't slide: the top row lands on the bottom row; when a pair of partners meets, both squares change colour.
   • If the mirror is diagonal, turn the paper until the mirror is upright, then find the partners.
2. 2

   Exactly N lines: complete the family, then check

   ▶ 4:10

   When to use it: The question wants a pattern with exactly a given number of lines of symmetry (exactly two or four) and asks for the fewest extra squares to shade or change; the lines are not drawn, so you work out which ones they are.

   • A square has at most 4 lines of symmetry: across, down and the two diagonals.
   • A square and all its partners form a family: if you colour one, colour the whole family.
   • Exactly 2 lines means one pair: across and down, or the two diagonals (one across plus one diagonal gives all 4); try both pairs.
   • After filling in, always check how many lines you have: too few, add; too many, break; use the cheaper pair.