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合同
面積が同じで、かつ、形も同じ図形は、合同(ごうどう)になる。
例えば、\( \bigtriangleup ABC \) と\( \bigtriangleup DEF \) は、合同になる。
面積も形も、同じなので、合同になる。
\begin{xy}
(0,0)*{A}="A",
(0,-27)*{C}="A",
(15,-27)*{B}="A",
(2,-14)*{6}="A",
(8,-20.5)*{4}="A",
{(0,-3) \ar @{-}(0,-23)},
{(0,-23) \ar @{-}(15,-23)},
{(0,-3) \ar @{-}(15,-23)},
{(2,-21) \ar @{-}(2,-23)},
{(2,-21) \ar @{-}(0,-21)},
(30,0)*{D}="A",
(30,-27)*{F}="A",
(45,-27)*{E}="A",
(32,-14)*{6}="A",
(38,-20.5)*{4}="A",
{(30,-3) \ar @{-}(30,-23)},
{(30,-23) \ar @{-}(45,-23)},
{(30,-3) \ar @{-}(45,-23)},
{(32,-21) \ar @{-}(32,-23)},
{(32,-21) \ar @{-}(30,-21)},
\end{xy}
しかし、\( \bigtriangleup ABC \) と\( \bigtriangleup GHI \) は、合同ではない。
面積は同じだが、形は同じではないので、合同ではない。
\begin{xy}
(0,0)*{A}="A",
(0,-27)*{C}="A",
(15,-27)*{B}="A",
(2,-14)*{6}="A",
(8,-20.5)*{4}="A",
{(0,-3) \ar @{-}(0,-23)},
{(0,-23) \ar @{-}(15,-23)},
{(0,-3) \ar @{-}(15,-23)},
{(2,-21) \ar @{-}(2,-23)},
{(2,-21) \ar @{-}(0,-21)},
(30,-10)*{G}="A",
(30,-27)*{I}="A",
(53,-27)*{H}="A",
(32,-18)*{3}="A",
(42,-26)*{8}="A",
{(30,-13) \ar @{-}(30,-23)},
{(30,-23) \ar @{-}(55,-23)},
{(30,-13) \ar @{-}(55,-23)},
{(32,-21) \ar @{-}(32,-23)},
{(32,-21) \ar @{-}(30,-21)},
\end{xy}
合同の記号
合同は、数学の記号で、\( \equiv \) と、書く。
例えば、合同な図形、\( \bigtriangleup ABC \) と\( \bigtriangleup DEF \) は、\( \bigtriangleup ABC \equiv \bigtriangleup DEF \) と、書く。
合同の記号( \( \equiv \) )は、等号( = )に、さらに横線を1本追加し、3本の横線になっている。
\begin{xy}
(20,10)*{\bigtriangleup ABC \equiv \bigtriangleup DEF}="A",
(0,0)*{A}="A",
(0,-27)*{C}="A",
(15,-27)*{B}="A",
(2,-14)*{6}="A",
(8,-20.5)*{4}="A",
{(0,-3) \ar @{-}(0,-23)},
{(0,-23) \ar @{-}(15,-23)},
{(0,-3) \ar @{-}(15,-23)},
{(2,-21) \ar @{-}(2,-23)},
{(2,-21) \ar @{-}(0,-21)},
(30,0)*{D}="A",
(30,-27)*{F}="A",
(45,-27)*{E}="A",
(32,-14)*{6}="A",
(38,-20.5)*{4}="A",
{(30,-3) \ar @{-}(30,-23)},
{(30,-23) \ar @{-}(45,-23)},
{(30,-3) \ar @{-}(45,-23)},
{(32,-21) \ar @{-}(32,-23)},
{(32,-21) \ar @{-}(30,-21)},
\end{xy}
また、合同な図形は、頂点の順番を、対応させて書かなければいけない。
例えば、\( \bigtriangleup ABC \equiv \bigtriangleup DEF \) は正しいが、\( \bigtriangleup ABC \equiv \bigtriangleup DFE \) は間違いだ。
きちんと頂点を対応させて\( \bigtriangleup ACB \equiv \bigtriangleup DFE \) と書けば、正しくなる。
<例題 \( \Large 1 \) >\( \bigtriangleup ABC \) と合同な3角形を見つけ、合同の記号で表しなさい。なお、対応する頂点の順番には、気をつけなさい。
\begin{xy}
(0,0)*{A}="A",
(0,-27)*{C}="A",
(15,-27)*{B}="A",
(2,-14)*{6}="A",
(8,-20.5)*{4}="A",
{(0,-3) \ar @{-}(0,-23)},
{(0,-23) \ar @{-}(15,-23)},
{(0,-3) \ar @{-}(15,-23)},
{(2,-21) \ar @{-}(2,-23)},
{(2,-21) \ar @{-}(0,-21)},
(30,0)*{G}="A",
(45,-27)*{I}="A",
(45,0)*{H}="A",
(42.5,-14)*{6}="A",
(38,-6)*{4}="A",
{(30,-3) \ar @{-}(45,-3)},
{(30,-3) \ar @{-}(45,-23)},
{(45,-3) \ar @{-}(45,-23)},
{(43,-3) \ar @{-}(43,-5)},
{(45,-5) \ar @{-}(43,-5)},
\end{xy}
\begin{xy}
(0,0)*{J}="A",
(0,-20)*{L}="A",
(21,-20)*{K}="A",
(2,-8)*{4}="A",
(11,-14)*{6}="A",
{(0,-3) \ar @{-}(0,-16)},
{(0,-16) \ar @{-}(23,-16)},
{(0,-3) \ar @{-}(23,-16)},
{(2,-14) \ar @{-}(2,-16)},
{(2,-14) \ar @{-}(0,-14)},
(31,-27)*{O}="A",
(45,-27)*{N}="A",
(45,0)*{M}="A",
(42.5,-14)*{6}="A",
(38,-20.5)*{4}="A",
{(30,-23) \ar @{-}(45,-3)},
{(30,-23) \ar @{-}(45,-23)},
{(45,-3) \ar @{-}(45,-23)},
{(43,-23) \ar @{-}(43,-21)},
{(43,-21) \ar @{-}(45,-21)},
\end{xy}
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