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第156頁

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證明：?$ $?在?$△ ADC $?和?$△A_1\ \mathrm {D}_1\ \mathrm {C}_1 $?中
?$ \begin {cases}{A D=A_1\ \mathrm {D}_1}\\{D C=D_1\ \mathrm {C}_1 }\\{A C=A_1\ \mathrm {C}_1}\end {cases}$?
∴?$△A D C ≌△A_1\ \mathrm {D}_1\ \mathrm {C}_1(S S S) $?
又在?$△ABC $?和?$ △A_1\ \mathrm {B}_1\ \mathrm {C}_1 $?中
?$\begin {cases}{A B=A_1\ \mathrm {B}_1}\\{B C=B_1\ \mathrm {C}_1 }\\{A C=A_1\ \mathrm {C}_1}\end {cases}$?
∴?$△A B C≌△A_1\ \mathrm {B}_1\ \mathrm {C}_1(S S S) $?
∴?$∠B =∠B_1$?，?$ ∠B A D=∠B_1\ \mathrm {A}_1\ \mathrm {D}_1 ∠D=∠D_1 $?，
?$∠BCD=∠B_1\ \mathrm {C}_1\ \mathrm {D}_1 $?
∴四邊形?$ ABCD $?與四邊形?$ A_1\ \mathrm {B}_1\ \mathrm {C}_1\ \mathrm {D}_1 $?全等
解?$ ∶ ∠A=∠A_1$?
理由：連接?$ B D $?、?$ B_1\ \mathrm {D}_1$?
在?$ △ABD $?和?$△A_1\ \mathrm {B}_1\ \mathrm {D}_1 $?中
?$\begin {cases}{A D=A_1\ \mathrm {D}_1}\\{∠A=∠A_1 }\\{A B=A_1\ \mathrm {B}_1}\end {cases}$?
∴?$△A B D ≌△ A_1\ \mathrm {B}_1\ \mathrm {D}_1(S A S)$?
∴?$B D=B_1\ \mathrm {D}_1$?
由?$ (1 ) $?可知四邊形?$ ABCD$?與四邊形?$ A_1\ \mathrm {B}_1\ \mathrm {C}_1\ \mathrm {D}_1 $?全等?$.$?
解：條件?$ A C=A_1\ \mathrm {C}_1$?，?$ A D=A_1\ \mathrm {D}_1$?
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