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>A 3角形の合同条件

3角形の合同条件

3角形の合同条件は、3つある。


合同条件1:1組の辺と、その両端の角が、それぞれ等しい。(1辺両端角相等(いっぺんりょうたんかくそうとう))

\begin{xy} {(5,0) \ar @{-}(0,-15)}, {(25,-15) \ar @{-}(0,-15)}, {(5,0) \ar @{-}(25,-15)}, {(12,-13.5) \ar @{-}(12,-16.5)}, (20,-13.5)*{\scriptsize 〇}="A", (3,-13)*{\small ●}="A", {(35,0) \ar @{-}(30,-15)}, {(55,-15) \ar @{-}(30,-15)}, {(35,0) \ar @{-}(55,-15)}, {(42,-13.5) \ar @{-}(42,-16.5)}, (50,-13.5)*{\scriptsize 〇}="A", (33,-13)*{\small ●}="A", \end{xy}

合同条件2:2組の辺と、その間の角が、それぞれ等しい(2辺挟角相等(にへんきょうかくそうとう))

\begin{xy} {(5,0) \ar @{-}(0,-15)}, {(25,-15) \ar @{-}(0,-15)}, {(5,0) \ar @{-}(25,-15)}, {(12,-13) \ar @{-}(12,-17)}, (20,-13.5)*{\scriptsize 〇}="A", {(12,-7) \ar @{-}(14,-5)}, {(13,-8) \ar @{-}(15,-6)}, {(35,0) \ar @{-}(30,-15)}, {(55,-15) \ar @{-}(30,-15)}, {(35,0) \ar @{-}(55,-15)}, {(42,-13.5) \ar @{-}(42,-16.5)}, (50,-13.5)*{\scriptsize 〇}="A", {(42,-7) \ar @{-}(44,-5)}, {(43,-8) \ar @{-}(45,-6)}, \end{xy}

合同条件3:3組の辺が、それぞれ等しい(3辺相等(さんぺんそうとう))

\begin{xy} {(5,0) \ar @{-}(0,-15)}, {(25,-15) \ar @{-}(0,-15)}, {(5,0) \ar @{-}(25,-15)}, {(12,-13) \ar @{-}(12,-17)}, {(12,-7) \ar @{-}(14,-5)}, {(13,-8) \ar @{-}(15,-6)}, {(12,-7) \ar @{-}(14,-5)}, {(13,-8) \ar @{-}(15,-6)}, {(2,-4.5) \ar @{-}(5,-5.5)}, {(1.5,-5.5) \ar @{-}(4.5,-6.5)}, {(1,-6.5) \ar @{-}(4,-7.5)}, {(35,0) \ar @{-}(30,-15)}, {(55,-15) \ar @{-}(30,-15)}, {(35,0) \ar @{-}(55,-15)}, {(42,-13.5) \ar @{-}(42,-16.5)}, {(42,-7) \ar @{-}(44,-5)}, {(43,-8) \ar @{-}(45,-6)}, {(32,-4.5) \ar @{-}(35,-5.5)}, {(31.5,-5.5) \ar @{-}(34.5,-6.5)}, {(31,-6.5) \ar @{-}(34,-7.5)}, \end{xy}

3角形の合同は、辺と角を合わせて、3つの材料が必要だと、覚えておきましょう。



<例題 \( \Large 1 \) >以下から合同な3角形を見つけ、合同の記号で表しなさい。また、合同条件も、書きなさい。

\begin{xy} (10,2)*{\small A}="A", (0,-16)*{\small C}="A", (25,-16)*{\small B}="A", (13,-16)*{\small 5}="A", (19,-5)*{\small 4}="A", (3,-5)*{\small 3}="A", {(10,0) \ar @{-}(0,-13)}, {(25,-13) \ar @{-}(0,-13)}, {(10,0) \ar @{-}(25,-13)}, (30,2)*{\small D}="A", (55,2)*{\small E}="A", (40,-16)*{\small F}="A", (41,2)*{\small 5}="A", (47,-9)*{\small 4}="A", (46,-3)*{\scriptsize 40^\circ}="A", {(40,-13) \ar @{-}(30,0)}, {(55,0) \ar @{-}(30,0)}, {(40,-13) \ar @{-}(55,0)}, (50,0.5)*{}="E"; (52,-3.3)*{}="F"; "E"; "F" **\crv{(49,-2)}; \end{xy} \begin{xy} (13,2)*{\small G}="A", (0,-16)*{\small I}="A", (25,-16)*{\small H}="A", (13,-16)*{\small 5}="A", (18,-11)*{\scriptsize 55^\circ}="A", (8,-11)*{\scriptsize 45^\circ}="A", {(13,0) \ar @{-}(0,-13)}, {(25,-13) \ar @{-}(0,-13)}, {(13,0) \ar @{-}(25,-13)}, (4,-13.5)*{}="E"; (3,-9)*{}="F"; "E"; "F" **\crv{(5,-11)}; (21,-13.5)*{}="E"; (22,-9)*{}="F"; "E"; "F" **\crv{(20,-11)}; (30,2)*{\small J}="A", (45,-16)*{\small L}="A", (55,2)*{\small K}="A", (43,2)*{\small 5}="A", (51.5,-7)*{\small 4}="A", (35,-7)*{\small 3}="A", {(45,-13) \ar @{-}(30,0)}, {(55,0) \ar @{-}(30,0)}, {(45,-13) \ar @{-}(55,0)}, \end{xy} \begin{xy} (0,2)*{\small M}="A", (25,2)*{\small N}="A", (15,-16)*{\small O}="A", (13,2)*{\small 5}="A", (7,-9)*{\small 4}="A", (8,-3)*{\scriptsize 40^\circ}="A", {(15,-13) \ar @{-}(0,0)}, {(25,0) \ar @{-}(0,0)}, {(15,-13) \ar @{-}(25,0)}, (5,0.5)*{}="E"; (3,-3.3)*{}="F"; "E"; "F" **\crv{(5,-2)}; (43,-16)*{\small R}="A", (30,2)*{\small P}="A", (55,2)*{\small Q}="A", (43,2)*{\small 5}="A", (48,-2)*{\scriptsize 55^\circ}="A", (38,-2)*{\scriptsize 45^\circ}="A", {(43,-13) \ar @{-}(30,0)}, {(55,0) \ar @{-}(30,0)}, {(43,-13) \ar @{-}(55,0)}, (34,+0.5)*{}="E"; (33,-4)*{}="F"; "E"; "F" **\crv{(35,-2)}; (51,+0.5)*{}="E"; (52,-4)*{}="F"; "E"; "F" **\crv{(50,-2)}; \end{xy}


<解答 \( \Large 1 \) >
\( \bigtriangleup ABC \equiv \bigtriangleup LKJ \)
合同条件:3組の辺が、それぞれ等しい。

\( \bigtriangleup DEF \equiv \bigtriangleup NMO \)
合同条件:2組の辺と、その間の角が、それぞれ等しい。

\( \bigtriangleup GHI \equiv \bigtriangleup RQP \)
合同条件:1組の辺と、その両端の角が、それぞれ等しい。

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