1Congruent means "exactly the same shape and size"
If two shapes overlap perfectly when placed on top of each other, those two shapes are congruent. The mirrored or rotated image used to make a symmetric shape is always congruent to the original.
2A line-symmetric shape matches "its reflection in a mirror"
Draw a line through the middle of a shape and fold along it — if both halves match perfectly, it's line symmetric. That line is called the axis of symmetry. Neat shapes like a square are the classic example.
3A point-symmetric shape matches "itself rotated 180°"
Mark a point at the center of a shape and spin it 180° around that point — if it matches the original shape perfectly, it's point symmetric. That marked point is called the center of symmetry. A parallelogram is the classic example.
4Line symmetry and point symmetry are different properties
Some shapes have both line and point symmetry (a square), some have line symmetry but not point symmetry (an isosceles trapezoid), and some are the reverse (a parallelogram). Some shapes have neither.
Don't decide just from the feeling that something "looks neat" — get in the habit of actually mirroring or rotating it to check whether it matches perfectly, and you won't get confused.
5Try this
- Try both modes on each shape, one at a time. See how the same shape can give different results for line symmetry versus point symmetry.
- Guess before you check. Before clicking the button, decide for yourself whether "this shape will match," then compare with the actual result.
- Meet all four cases in the quiz. Practice telling apart: line symmetric only, point symmetric only, both, and neither.