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Angles on Parallel Lines Theory
![\begin{multicols}{2} Alternate angles on parallel lines are equal. \columnbreak \resizebox{0.4\textwidth}{!}{ \begin{tikzpicture} \def \belowleft{} \def \belowright{} \def \aboveleft{} \def \aboveright{} \def \angleabove{} \def \anglebelow{} \def \angle{110} \draw[draw=none,line width=1pt] (0,0) -- (\angle:.5cm) arc (\angle:180:.5cm) node[midway] {\(d\)}; \draw[draw=none,line width=1pt] (0,0) -- (right:.5cm) arc (0:\angle:.5cm) node[midway] {\(b\)}; \draw[draw=none,line width=1pt] (0,0) -- (right:.5cm) arc (0:-180+\angle:.5cm) node[midway] {}; \draw[draw=none,line width=1pt] (0,0) -- (180:.5cm) arc (180:180+\angle:.5cm) node[midway] {}; \begin{scope}[shift={(\angle:1.77cm)}] \draw[draw=none,line width=1pt] (0,0) -- (\angle:.5cm) arc (\angle:180:.5cm) node[midway] {}; \draw[draw=none,line width=1pt] (0,0) -- (right:.4cm) arc (0:\angle:.4cm) node[midway] {}; \draw[draw=none,line width=1pt] (0,0) -- (right:.6cm) arc (0:-180+\angle:.6cm) node[midway] {\(c\)}; \draw[draw=none,line width=1pt] (0,0) -- (180:.5cm) arc (180:180+\angle:.5cm) node[midway] {\(a\)}; \end{scope} \begin{scope}[line width=1pt,latex-latex] \draw (\angle:-1.3cm) node(E)[below] {$\anglebelow$} -- (\angle:3cm) node(F)[above] {$\angleabove$}; \draw (-2.5,0) node(A)[left] {$\belowleft$} -- (2.5,0) node(B)[right]{$\belowright$}; \draw[shift={(90:1.5cm)}] (-2.5,0) node(C)[left] {$\aboveleft$} -- (2.5,0) node(D)[right]{$\aboveright$}; \end{scope} \node (O) at (0,0){}; \node (OA) at (\angle:1.5){}; \node[draw=red,align=left] (B) at (4,0.5) {\(\Large\begin{aligned} a&=b\\ c&=d\\ \end{aligned}\)}; \end{tikzpicture}} \end{multicols} \begin{multicols}{2} Corresponding angles on parallel lines are equal. \columnbreak \resizebox{0.4\textwidth}{!}{ \begin{tikzpicture} \def \belowleft{} \def \belowright{} \def \aboveleft{} \def \aboveright{} \def \angleabove{} \def \anglebelow{} \def \angle{110} \draw[draw=none,line width=1pt] (0,0) -- (\angle:.5cm) arc (\angle:180:.5cm) node[midway] {\(f\)}; \draw[draw=none,line width=1pt] (0,0) -- (right:.5cm) arc (0:\angle:.5cm) node[midway] {\(b\)}; \draw[draw=none,line width=1pt] (0,0) -- (right:.5cm) arc (0:-180+\angle:.5cm) node[midway] {\(d\)}; \draw[draw=none,line width=1pt] (0,0) -- (180:.5cm) arc (180:180+\angle:.5cm) node[midway] {\(h\)}; \begin{scope}[shift={(\angle:1.77cm)}] \draw[draw=none,line width=1pt] (0,0) -- (\angle:.5cm) arc (\angle:180:.5cm) node[midway] {\(e\)}; \draw[draw=none,line width=1pt] (0,0) -- (right:.4cm) arc (0:\angle:.4cm) node[midway] {\(a\)}; \draw[draw=none,line width=1pt] (0,0) -- (right:.6cm) arc (0:-180+\angle:.6cm) node[midway] {\(c\)}; \draw[draw=none,line width=1pt] (0,0) -- (180:.5cm) arc (180:180+\angle:.5cm) node[midway] {\(g\)}; \end{scope} \begin{scope}[line width=1pt,latex-latex] \draw (\angle:-1.3cm) node(E)[below] {$\anglebelow$} -- (\angle:3cm) node(F)[above] {$\angleabove$}; \draw (-2.5,0) node(A)[left] {$\belowleft$} -- (2.5,0) node(B)[right]{$\belowright$}; \draw[shift={(90:1.5cm)}] (-2.5,0) node(C)[left] {$\aboveleft$} -- (2.5,0) node(D)[right]{$\aboveright$}; \end{scope} \node (O) at (0,0){}; \node (OA) at (\angle:1.5){}; \node[draw=red,align=left] (B) at (4,0.5) {\(\Large\begin{aligned} a&=b\\ c&=d\\ e&=f\\ g&=h \end{aligned}\)}; \end{tikzpicture}} \end{multicols} \begin{multicols}{2} Co-interior angles on parallel lines are supplementary. \columnbreak \resizebox{0.4\textwidth}{!}{ \begin{tikzpicture} \def \belowleft{} \def \belowright{} \def \aboveleft{} \def \aboveright{} \def \angleabove{} \def \anglebelow{} \def \angle{110} \draw[draw=none,line width=1pt] (0,0) -- (\angle:.5cm) arc (\angle:180:.5cm) node[midway] {\(d\)}; \draw[draw=none,line width=1pt] (0,0) -- (right:.5cm) arc (0:\angle:.5cm) node[midway] {\(b\)}; \draw[draw=none,line width=1pt] (0,0) -- (right:.5cm) arc (0:-180+\angle:.5cm) node[midway] {}; \draw[draw=none,line width=1pt] (0,0) -- (180:.5cm) arc (180:180+\angle:.5cm) node[midway] {}; \begin{scope}[shift={(\angle:1.77cm)}] \draw[draw=none,line width=1pt] (0,0) -- (\angle:.5cm) arc (\angle:180:.5cm) node[midway] {}; \draw[draw=none,line width=1pt] (0,0) -- (right:.4cm) arc (0:\angle:.4cm) node[midway] {}; \draw[draw=none,line width=1pt] (0,0) -- (right:.6cm) arc (0:-180+\angle:.6cm) node[midway] {\(c\)}; \draw[draw=none,line width=1pt] (0,0) -- (180:.5cm) arc (180:180+\angle:.5cm) node[midway] {\(a\)}; \end{scope} \begin{scope}[line width=1pt,latex-latex] \draw (\angle:-1.3cm) node(E)[below] {$\anglebelow$} -- (\angle:3cm) node(F)[above] {$\angleabove$}; \draw (-2.5,0) node(A)[left] {$\belowleft$} -- (2.5,0) node(B)[right]{$\belowright$}; \draw[shift={(90:1.5cm)}] (-2.5,0) node(C)[left] {$\aboveleft$} -- (2.5,0) node(D)[right]{$\aboveright$}; \end{scope} \node (O) at (0,0){}; \node (OA) at (\angle:1.5){}; \node[draw=red,align=left] (B) at (5,0.5) {\(\Large\begin{aligned} a+d&=180^{\circ}\\ c+b&=180^{\circ}\\ \end{aligned}\)}; \end{tikzpicture}} \end{multicols}](/media/wlcjlrb2/9213.png)
NSW Y8 Maths Geometry Angles on Parallel Lines
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