I’ve come across a geometry problem which I think doesn’t have an answer. Am I wrong?
Here’s the problem:
Which of the following shapes cannot be obtained by cutting a parallelogram into two congruent pieces and rearranging into one?
A. Square (eliminated:base=height)
B. Rectangle (eliminated)
C. Rhombus (Xtra tricky but still eliminated:side AB=4$\times$side BC)
D. Parallelogram (eliminated)  Note by Jeff Giff
1 year, 1 month ago

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Your solution definitely seems viable, maybe they meant that one shape can't be formed from any arbitrary parallelogram? In your examples you relied on certain proportions in the shape, so it might be the case that a construction doesn't exist for all parallelograms to turn into one of those shapes.

I think you can still eliminate rectangle and parallelogram though, because there can only be one answer and if either B or D were impossible, A or C would have to be as well.

- 1 year, 1 month ago