brinlin
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Taking $B$ as the origin, let $A,C,D$ be represented by vectors $\def\v{\mathbf} \v a,\v c,\v d$. You are told that $AB = BC$, which says that $\v{a.a} = \v{c.c}$. Also, $CD = DA$, so that $(\v d - \v c)\v.(\v d - \v c) = (\v d - \v a)\v.(\v d - \v a)$. Using those equations, you want to show that $AC = BD$, or in other words $(\v c - \v a).\v d = \v 0$.brinlin said:
By choosing $A$ and $C$ to be on the $x$-axis, and $B$ and $D$ to be on the $y$-axis, you are assuming that $AC$ is perpendicular to $BD$, which is what you are supposed to be proving.Country Boy said:I would label the point where AC and BD intersect "E" and let that be the origin. Then A is (-a, 0) for some number, a, and C is (a, 0). B is (0, b) and D is (0,-d) ...