karl
New Member
Posts: 2
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Post by karl on Mar 2, 2020 18:42:56 GMT
Hello,
I'm not sure but I propose the Following demonstration: 1) If ABCD is a rectangle, it is meaning that each edge at right angle. 2) To prove it, I propose to prove that the each opposed edge on the unity circle pass are placed on a line passing through the center. 3) For example, if A=-C and B=-D => (A,C) and (B,D) are on a stright line through the center and thanks to the Thales theorem, A, B, C and D have right angle. 4) If ABCD is a rectangle: (a) A=-C (b) B=-D (a) + (b) A+B = -(C+D) <=> A+B+C+D=0 Done!
(It is my first time that I'm trying to demonstrate somethink)
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Post by Admin on Mar 3, 2020 9:51:39 GMT
Hello, I'm not sure but I propose the Following demonstration: 1) If ABCD is a rectangle, it is meaning that each edge at right angle. 2) To prove it, I propose to prove that the each opposed edge on the unity circle pass are placed on a line passing through the center. 3) For example, if A=-C and B=-D => (A,C) and (B,D) are on a stright line through the center and thanks to the Thales theorem, A, B, C and D have right angle. 4) If ABCD is a rectangle: (a) A=-C (b) B=-D (a) + (b) A+B = -(C+D) <=> A+B+C+D=0 Done! (It is my first time that I'm trying to demonstrate somethink) Hi karl This seems OK but don't forget that the exercise says: Given that $A+B+C+D=0$ show that $ABCD$ is a rectangle, so we only need to assume $A+B+C+D=0$ and show $A+B+C+D=0\Rightarrow ABCD$ is a rectangle. Vasco
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karl
New Member
Posts: 2
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Post by karl on Mar 3, 2020 10:17:40 GMT
You're right!
Thanks.
Karl (sorry for my english but I coming from France)
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