Rhombus
Two rhombi
Type	quadrilateral , bipyramid
Edges and vertices	4
Schlafli symbol	{ } + { } or 2{ }
Coxeter diagram	?????????:CDD
Symmetry group	Dih 2 , [2], (*22), order 4
Area	${\displaystyle {\tfrac {pq}{2}}}$
Dual polygon	rectangle
Properties	convex , isotoxal
←3 4 5→

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• ????????? ${\displaystyle S={\frac {1}{2}}(a\times b)=c\cdot h=c^{2}\sin {\alpha }}$
• ???????? ${\displaystyle P=4c=2{\sqrt {a^{2}+b^{2}}}}$
• ????? ${\displaystyle c={\frac {1}{2}}{\sqrt {a^{2}+b^{2}}}}$

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???????? A, B, C ??? D ?????????????????????? ????? AC ??? BD ?????????????????????????? ??????? ${\displaystyle {\overrightarrow {AB}}}$ ???????? ??????? ?? A ?? B ???

${\displaystyle {\overrightarrow {AC}}={\overrightarrow {AB}}+{\overrightarrow {BC}}}$

${\displaystyle {\overrightarrow {BD}}={\overrightarrow {BC}}+{\overrightarrow {CD}}={\overrightarrow {BC}}-{\overrightarrow {AB}}}$    (??????? ${\displaystyle {\overrightarrow {AB}}}$ ???????? ${\displaystyle {\overrightarrow {CD}}\qquad \Rightarrow {\overrightarrow {CD}}=-{\overrightarrow {AB}}}$)

??????? ???????????? ??????????? ${\displaystyle {\overrightarrow {AC}}}$ ??? ??????? ${\displaystyle {\overrightarrow {BD}}}$ ?????

${\displaystyle {\begin{aligned}{\overrightarrow {AC}}\cdot {\overrightarrow {BD}}&=({\overrightarrow {AB}}+{\overrightarrow {BC}})({\overrightarrow {BC}}-{\overrightarrow {AB}})\\&=({\overrightarrow {AB}}\cdot {\overrightarrow {BC}})-({\overrightarrow {AB}}\cdot {\overrightarrow {AB}})+({\overrightarrow {BC}}\cdot {\overrightarrow {BC}})-({\overrightarrow {BC}}\cdot {\overrightarrow {AB}})\\&=0\end{aligned}}}$

${\displaystyle \therefore \quad {\overrightarrow {AC}}\perp {\overrightarrow {BD}}}$

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