Write an indirect proof proving the four angles of a square add up to 360°.

Question

anonymous · Answer

@jim_thompson5910  Hi , Do you mind helping me with this?

jim_thompson5910 · Answer

how far did you get?

anonymous · Answer

Well I saw this post definition of square: a quadrilateral with four equal sides and four right angles
right angles = 90 degrees
4 angles * 90 degrees = 360 degrees

anonymous · Answer

http://openstudy.com/study#/updates/525c1638e4b002bdb09055d1 Just wanted to know if that was all I would need to say.

jim_thompson5910 · Answer

well when it comes to indirect proofs you assume the opposite is true

so you assume "four angles of a square do NOT add up to 360"

jim_thompson5910 · Answer

then you go about proving that brings a contradiction

so the opposite of  "four angles of a square do NOT add up to 360" is true

which means  "four angles of a square do add up to 360" has to be true

anonymous · Answer

Draw any of the diagonal of the quadrilateral and thus you get quadrilateral divided into two triangles ...
as no angles are formed within the quadrilateral..
so the summ of the angles of the quadrilateral = sum of the interior angles of triangle1 and sum of the interior angles of the triangle2
=180+180...
(sum of the interior angles of the triangle add upto 180)

anonymous · Answer

Ok I see what you both are saying. So would what matricked said be an indirect proof?

jim_thompson5910 · Answer

that's another (actually better) way to do it

anonymous · Answer

Ok so that is a indirect proof?

anonymous · Answer

@matricked

jim_thompson5910 · Answer

to do it indirectly, you have to start with the opposite and prove it brings about a contradiction

anonymous · Answer

But I don't know how to start opposite :(

jim_thompson5910 · Answer

take the initial claim and completely negate it

jim_thompson5910 · Answer

four angles of a square add up to 360°

is the initial claim

jim_thompson5910 · Answer

so the opposite of that is ???

anonymous · Answer

Four angles of a square do not add up to 360 degrees

jim_thompson5910 · Answer

yep

jim_thompson5910 · Answer

show that results in a contradiction

anonymous · Answer

Is it okay if you help walk me through it?

jim_thompson5910 · Answer

sure

jim_thompson5910 · Answer

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jim_thompson5910 · Answer

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jim_thompson5910 · Answer

add in the following angle labels

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jim_thompson5910 · Answer

what do these angles add up to

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