## Gabylovesyou one year ago 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.

1. Gabylovesyou

@ganeshie8 @phi @AccessDenied

2. phi

Here is what an indirect proof means http://regentsprep.org/Regents/math/geometry/GP3b/indirectlesson.htm

3. Gabylovesyou

ok.. so i would first start with A rectangle doesn't have congruent diagonals

4. phi

yes. That is as far as I got so far.

5. Gabylovesyou

lol! what happens next ? ;s

6. phi

draw a picture of a rectangle, label the sides , show the right angles. draw in a diagonal

7. Gabylovesyou

|dw:1396376755171:dw|

8. phi

show the angles are all 90º

9. Gabylovesyou

|dw:1396376914251:dw|

10. 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.

11. Gabylovesyou

ok

12. phi

|dw:1396377047759:dw|

13. phi

does that make sense (so far ?)

14. Gabylovesyou

yes

15. phi

we could do the same thing for the other diagonal |dw:1396377220075:dw|

16. 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.

17. Gabylovesyou

the equal sign thing means does not equal ?

18. phi

yes, ≠ means does not equal

19. Gabylovesyou

ok so i tried doing it in my own words... im going to put it and then delete it

20. Gabylovesyou

@phi

21. Gabylovesyou

@phi DONT LEAVE ME haha

22. 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

23. Gabylovesyou

thanks