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  • Oh my gosh, I don't understand geometry! I see this everywhere, if I were to measure he sides of these quadrilaterals and prove them to be parallelograms. I could show my friends that these everyday shapes are in the world of geometry.
  • Oh, well sure! The diagonals are congruent because the square has all the properties of all other parallelograms. In order for it to be a square, it has to have congruent diagonals and vice versa. But in many cases, you will need much more than congruent diagonals to prove a parallelogram a square.
  • Hey Charlotte, do you think you can explain this to me? I still don't understand what he is saying, why are the diagonals of a square congruent?  
  • Sorry to bother you again, but, do you know what the proof would be like if I have 1 pair of sides opposite and congruent and I am trying to prove that its a parallelogram.
  • Okay, so the proof would somewhat be like this: The statement would be the given and then you add the next step, this is a simple 2 step proof. Therefore the next step would be stating the statement that shape whatever its named is a parallelogram since it has one pair of both opposite AND parallel sides, it's a parallelogram.  
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