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Write an indirect proof to show that a rectangle has congruent diagonals. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted.

Mathematics
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  • phi
Here is what an indirect proof means http://regentsprep.org/Regents/math/geometry/GP3b/indirectlesson.htm
ok.. so i would first start with A rectangle doesn't have congruent diagonals

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Other answers:

  • phi
yes. That is as far as I got so far.
lol! what happens next ? ;s
  • phi
draw a picture of a rectangle, label the sides , show the right angles. draw in a diagonal
|dw:1396376755171:dw|
  • phi
show the angles are all 90º
|dw:1396376914251:dw|
  • phi
the first thing that comes to mind is using pythagoras to find the length of a diagonal that leads to a direct proof. maybe we can tweak it to make in indirect.
ok
  • phi
|dw:1396377047759:dw|
  • phi
does that make sense (so far ?)
yes
  • phi
we could do the same thing for the other diagonal |dw:1396377220075:dw|
  • phi
if the diagonals are not equal to each other, that means a^2+b^2 ≠ a^2 + b^2 and that would only happen if we were not allowed to use the pythagorean theorem. But we have a right triangle (with 90º angle) so we are allowed. therefore our assumption that the diagonals are different must be wrong. that sure sounds convoluted, but it's the best I can come up with.
the equal sign thing means does not equal ?
  • phi
yes, ≠ means does not equal
ok so i tried doing it in my own words... im going to put it and then delete it
@phi DONT LEAVE ME haha
  • phi
I would change that means that a^2 + b^2 does not equal a^2 + b^2 if we are not allowed to that means that a^2 + b^2 does not equal a^2 + b^2 SO we are not allowed
thanks

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