Resources for Testing for Right Angled Triangles
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Questions
6
With Worked SolutionClick Here -
Video Tutorials
2
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Testing for Right Angled Triangles Theory
![\begin{multicols}{2} \textbf{Example 1}\\ Determine if \(\triangle ABC\) is right-angled\\ \begin{center} \begin{tikzpicture}[scale=0.5] \coordinate[label=below right:B] (O) at (0,0); \coordinate[label=above:A] (A) at (0,8); \coordinate[label=below left:C] (B) at (-3,0); \draw[line width=1pt] (O)--(B)node[midway ,below] {11}--(A)node[left=4pt,midway]{61}--(O) node[midway,right] {60}; \pic [draw=black,line width=1pt,angle radius=0.4cm,angle eccentricity=1.6,""] {right angle=B--O--A}; \end{tikzpicture} \end{center} \textbf{Example 1 solution}\\ If right-angled then\\ \(\begin{aligned} AB^2+BC^2 & =AC^2 \\ AB^2+BC^2 & =60^2+11^2 \\ & =3721 \\ \end{aligned}\)\\ \(\begin{aligned} AC^2 & =61^2 \\ & =3721 \end{aligned}\)\\ \(\begin{aligned} \therefore AB^2+BC^2 & =AC^2 \end{aligned}\)\\ \(\therefore \triangle ABC\) is right-angled. \columnbreak \textbf{Example 2}\\ Determine if \(\triangle ABC\) is right-angled\\ \begin{center} \begin{tikzpicture}[scale=0.5] \coordinate[label=below right:B] (O) at (0,0); \coordinate[label=above:A] (A) at (0,3); \coordinate[label=below left:C] (B) at (-8,0); \draw[line width=1pt] (O)--(B)node[midway ,below] {70}--(A)node[above left, midway]{71}--(O) node[midway,right] {13}; \pic [draw=black,line width=1pt,angle radius=0.4cm,angle eccentricity=1.6,""] {right angle=B--O--A}; \end{tikzpicture} \end{center} \textbf{Example 2 solution}\\ If right-angled then\\ \(\begin{aligned} A B^2+B C^2 & =A C^2 \\ A B^2+B C^2 & =13^2+70^2 \\ & =5069 \end{aligned}\)\\ \(\begin{aligned} A C^2 & =71^2 \\ & =5041 \end{aligned}\)\\ \(\therefore A B^2+B C^2 \neq A C^2\)\\[3pt] \(\therefore \triangle A B C\) is not right-angled \end{multicols}](/media/23em0anp/9232.png)