Resources for Classifying Triangles
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Classifying Triangles Theory
![A triangle with:\\ \textbf{i)} No sides equal to each other is classified as scalene.\\ \begin{center} \begin{tikzpicture}[scale=0.8] \coordinate (O) at (0,0); \coordinate (A) at (60:2cm); \coordinate (B) at (right:3cm); \draw[line width=1pt] (O)--(B)--(A)--(O); \end{tikzpicture} \end{center} \textbf{ii)} Two sides equal and corresponding angles equal to each other is classified as isosceles.\\ It has one axis of symmetry.\\ \begin{center} \begin{tikzpicture}[scale=0.8] \coordinate (O) at (0,0); \coordinate (A) at (2,2); \coordinate (B) at (4,0); \coordinate (D) at ($(O)!(A)!(B)$); \draw[line width=1pt,dashed,shorten >=-10pt,shorten <=-10pt] (A)--(D); \draw[line width=1pt] (O)--(B)--(A)node[midway,sloped]{|}--(O)node[midway,sloped]{|}; \pic [draw=black,line width=1pt,angle radius=0.6cm,angle eccentricity=1.6,""] {angle=B--O--A}; \pic [draw=black,line width=1pt,angle radius=0.6cm,angle eccentricity=1,""] {angle=A--B--O}; \begin{scope}[shift=(B)] \path (135:0.75) arc (135:180:0.75) node[midway,sloped] {\(\|\)}; \end{scope} \begin{scope}[shift=(O)] \path (0:0.75) arc (0:45:0.75) node[midway,sloped] {\(\|\)}; \end{scope} \end{tikzpicture} \end{center} \textbf{iii)} Three sides equal and corresponding angles equal to each other is classified as equilateral.\\ It has three axes of symmetry and rotational symmetry of order 3.\\ \begin{center} \begin{tikzpicture}[scale=0.8] \coordinate (O) at (0,0); \coordinate (A) at (2,2.83); \coordinate (B) at (4,0); \coordinate (C) at ($(O)!(A)!(B)$); \coordinate (D) at ($(A)!0.5!(B)$); \coordinate (E) at ($(O)!0.5!(A)$); \draw[line width=1pt,dashed,shorten >=-10pt,shorten <=-10pt] (A)--(C); \draw[line width=1pt,dashed,shorten >=-10pt,shorten <=-10pt] (O)--(D); \draw[line width=1pt,dashed,shorten >=-10pt,shorten <=-10pt] (B)--(E); \draw[line width=1pt] (O)--(B)node[pos=0.45,sloped]{|}--(A)node[pos=0.45,sloped]{|}--(O)node[pos=0.45,sloped]{|}; \pic [draw=black,line width=1pt,angle radius=0.6cm,angle eccentricity=1.6,""] {angle=B--O--A}; \pic [draw=black,line width=1pt,angle radius=0.6cm,angle eccentricity=1,""] {angle=A--B--O}; \begin{scope}[shift=(B)] \draw (125:0.75) arc (125:180:0.75) node[pos=0.5,sloped] {\(\|\)}; \end{scope} \begin{scope}[shift=(O)] \draw (0:0.75) arc (0:55:0.75) node[pos=0.5,sloped] {\(\|\)}; \end{scope} \pic [draw=black,line width=1pt,angle radius=0.6cm,angle eccentricity=1,""] {angle=O--A--B}; \begin{scope}[shift=(A)] \draw (245:0.75) arc (245:305:0.75) node[pos=0.5,sloped] {\(\|\)}; \end{scope} \end{tikzpicture} \end{center} \textbf{iv)} A triangle that contains a \(90^{\circ}\) angle is classified as right-angled.\\ \begin{center} \begin{tikzpicture}[scale=0.8] \coordinate (O) at (0,0); \coordinate (A) at (0,3); \coordinate (B) at (3,0); \draw[line width=1pt] (O)--(B)--(A)--(O); \pic [draw=black,line width=1pt,angle radius=0.4cm,angle eccentricity=1.6,""] {right angle=B--O--A}; \end{tikzpicture} \end{center}](/media/5j4fk3xg/9214.png)
NSW Y8 Maths Geometry Classifying Triangles
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Classifying Triangles - Video - Classifying Triangles 1
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Classifying Triangles - Video - Classifying Triangles 2
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