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If one draws two right triangles with a certain Δx and Δy as the legs and wants to prove that the connection of the two hypotenuses is a straight line, then should one prove that the angle between them is 180°?

http://uploadpic.org/storage/2011/thumb_em0Ys5txnYiOhPNXJVSS0UDJe.jpg

I have drawn the original picture in purple and then by SAS one can prove the two triangles congruent and then prove that the corresponding angles ∅ are congruent. Once one proves there is a right angle adjacent to it and a (90-∅) adjacent to that, the sum gives 180°.