Three moves

About this video

How many ways can you move a shape without stretching, shrinking or bending it? This animation shows the three, one after another, on squared paper. An L-shaped piece is first slid: every point moves the same distance in the same direction, and the arrows from its corners are all the same length and all parallel. On a grid you can say exactly how far it went, here 4 squares across and 1 up. Mathematicians call a slide a translation.

Next the L is turned a quarter turn, 90 degrees, about one fixed corner. That corner never moves, and every other corner travels round it along a circle. A turn is also called a rotation. Then the L is flipped across a dashed mirror line. Each corner lands on the other side, exactly as far from the line as it was: this is a reflection.

The slid and turned copies are still Ls, but the flipped copy is a J, its mirror image. The video then turns the J all the way round over the L, and it never fits. Only a flip changes which way round a shape is, which is why a left footprint can never be slid or turned into a right one. All three copies are congruent to the original: the same shape and the same size. This video goes with the Slides, Turns and Flips lesson of Geometry Level 1 on Knaph.

Transcript

1. 0:00Three ways to move a shape without changing it.
2. 0:09A slide. Every point moves the same way, the same distance.
3. 0:18On a grid you can say how far. Four across, one up.
4. 0:27A turn. The shape spins about one fixed point.
5. 0:36Every other point travels round it in a circle. Here, a quarter turn.
6. 0:46A flip. The shape goes across a mirror line.
7. 0:56Each point lands just as far from the line, on the other side.
8. 1:06After a slide or a turn, it's still the same way round.
9. 1:15But the flip made a mirror image. Turn it all you like. It never fits.
10. 1:26Like a left foot and a right foot.
11. 1:32All three copies are the same shape and size. They are congruent.
12. 1:42Slide, turn, flip. Only the flip turns it round.