Test Reflection Symmetry with a Fold
Use the supplied figure and proposed fold.
About 20 minutes, plus any extended practice
Supplied materials
- Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
- Supplied worked-case record: For a 6-by-4 rectangle, the vertical and horizontal lines through its center each make matching halves.
- All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.
Learn the idea
A line of symmetry reflects a whole figure onto itself. Imagine folding along the proposed line: the two halves must match in position and shape. Equal area alone is not enough. A nonsquare rectangle has two middle symmetry lines but generally does not have diagonal reflection symmetry.
Use the supplied figure and proposed fold. Compare where its corners and edges would land under reflection. Select the stated symmetry conclusion; use an ideal mathematical shape, not an imprecise hand-drawn version.
Test matching corner locations after reflection. Equal half-area does not by itself prove symmetry. Draw the proposed fold as a dashed line and pair reflected corners.
- Draw the proposed fold as a dashed line and pair reflected corners.
- Follow the worked example. Point to each number or shape feature and say what it tells you.
- Use the supplied figure and proposed fold.
- Try the question and then the three practice questions. Check your answers and explain any change you make.
See the method in action
For a 6-by-4 rectangle, the vertical and horizontal lines through its center each make matching halves. A diagonal fold does not align its unequal length and width edges, so it is not a symmetry line. A square’s equal side lengths allow its diagonal folds to match. Test matching corner locations after reflection. Equal half-area does not by itself prove symmetry. Draw the proposed fold as a dashed line and pair reflected corners.
Check your reasoning
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Helpful tips
- Test matching corner locations after reflection.
- Equal half-area does not by itself prove symmetry.
See the answer and explanation
4
Two center lines and two diagonals reflect the square onto itself.
Take it further
List the symmetry lines of an equilateral triangle. Expected: three lines, each through a vertex and the midpoint of the opposite side.
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More practice: try new cases
Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.
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Check the subject sources
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