



 
Hi Sonja. A rectangle is a quadrilateral with four right angles, so while it is useful to employ the idea of a parallelogram, it isn't necessary. The reason is in the unstated part of both your proposals: what connects a single right angle to all angles being right? If you show a parallelogram, you can use the properties of a parallelogram: opposite angles are equal, adjacent angles are supplementary. If you don't show a parallelogram, you can use the property of transversals across parallel lines: corresponding angles are supplementary (which you have to iterate one extra step for the opposite angle, or rely on a quadrilateral  3 right angles = 1 right angle). So in my assessment, it is easier to apply the higherorder properties of parallelograms than the more fundamental transversal properties, but the difference is in this step of the proof. An even simpler approach is this:
Hope this helps, PS: Check back at this URL in a couple of days; if other math consultants send other ideas, I'll post them here.  


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