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NSW Y8 Maths

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NSW Y8 Maths Geometry Angle Geometry

Resources for Angle Geometry

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Angle Geometry Theory

\begin{multicols}{2} Angles on a straight line add to \(180^{\circ}\).\\ They are called \textbf{supplementary angles} \columnbreak \begin{center} \begin{tikzpicture} \coordinate [label=above right:] (A) at (-2,0); \coordinate [label=below left:] (O) at (0,0); \coordinate [label=below left:] (O1) at (1,2); \coordinate [label=right:] (B) at (2,0); \draw[line width=1pt] (A)--(O)--(B); \draw[line width=1pt] (O)--(O1); \pic [draw=black,line width=1pt,angle radius=0.6cm,angle eccentricity=1.6,"$a$"] {angle=B--O--O1}; \pic [draw=black,line width=1pt,angle radius=0.6cm,angle eccentricity=1.6,"$b$"] {angle=O1--O--A}; \node[draw=red,line width=1pt, rectangle,align=left] at (2.5,1) {\(a+b=180^{\circ}\)}; \end{tikzpicture} \end{center} \end{multicols} \begin{multicols}{2} Angles that add to \(90^{\circ}\) are called complementary angles. \columnbreak \begin{center} \begin{tikzpicture} \coordinate [label=above right:] (A) at (0,2); \coordinate [label=below left:] (O) at (0,0); \coordinate [label=below left:] (O1) at (1.5,1.5); \coordinate [label=right:] (B) at (2.5,0); \draw[line width=1pt] (A)--(O)--(B); \draw[line width=1pt] (O)--(O1); \pic [draw=black,line width=1pt,angle radius=0.7cm,angle eccentricity=1.6,"$a$"] {angle=B--O--O1}; \pic [draw=black,line width=1pt,angle radius=0.7cm,angle eccentricity=1.6,"$b$"] {angle=O1--O--A}; \pic [draw=black,line width=1pt,angle radius=0.4cm,angle eccentricity=1.6,""] {right angle=B--O--A}; \node[draw=red,line width=1pt, rectangle,align=left] at (3.5,1) {\(a+b=90^{\circ}\)}; \end{tikzpicture} \end{center} \end{multicols} \begin{multicols}{2} Angles in a revolution add to \(360^{\circ}\). \columnbreak \begin{center} \begin{tikzpicture} \coordinate [label=above right:] (A) at (0,2); \coordinate [label=below left:] (O) at (0,0); \coordinate [label=below left:] (O1) at (1.5,1.5); \coordinate [label=right:] (B) at (-1,-1.5); \draw[line width=1pt] (A)--(O)--(B); \draw[line width=1pt] (O)--(O1); \pic [draw=black,line width=1pt,angle radius=0.7cm,angle eccentricity=1.6,"$b$"] {angle=B--O--O1}; \pic [draw=black,line width=1pt,angle radius=0.7cm,angle eccentricity=1.6,"$a$"] {angle=O1--O--A}; \pic [draw=black,line width=1pt,angle radius=0.7cm,angle eccentricity=1.6,"$c$"] {angle=A--O--B}; \node[draw=red,line width=1pt, rectangle,align=left] at (3.5,1) {\(a+b+c=360^{\circ}\)}; \end{tikzpicture} \end{center} \end{multicols} \begin{multicols}{2} Vertically opposite angles are equal. \columnbreak \begin{center} \begin{tikzpicture} \coordinate [label=above right:] (A) at (-1.5,1); \coordinate [label=below left:] (O) at (1.5,-1); \coordinate [label=below left:] (O1) at (1,1); \coordinate [label=below left:] (O2) at (0,0); \coordinate [label=right:] (B) at (-1,-1); \draw[line width=1pt] (A)--(O); \draw[line width=1pt] (B)--(O1); \pic [draw=black,line width=1pt,angle radius=0.5cm,angle eccentricity=1.6,"$a$"] {angle=A--O2--B}; \pic [draw=black,line width=1pt,angle radius=0.5cm,angle eccentricity=1.6,"$b$"] {angle=O--O2--O1}; \pic [draw=black,line width=1pt,angle radius=0.5cm,angle eccentricity=1.6,"$c$"] {angle=O1--O2--A}; \pic [draw=black,line width=1pt,angle radius=0.5cm,angle eccentricity=1.6,"$d$"] {angle=B--O2--O}; \node[draw=red,line width=1pt, rectangle,align=left] at (2.5,1) {\(a=b\)\\ \(c=d\)}; \end{tikzpicture} \end{center} \end{multicols}

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Videos

Videos relating to Angle Geometry.

  • Angle Geometry - Video - Vertically opposite angles

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  • Angle Geometry - Video - Angles at a Point

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  • Angle Geometry - Video - Supplementary Angles | Line and Angle Relationships

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