Resources for Tests for Congruent Triangles
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Tests for Congruent Triangles Theory
![\begin{multicols}{2} \(\triangle A B C\) is congruent to \(\triangle E O F\) \\ since the corresponding sides are all equal. $$ \text { i.e } \triangle A B C \equiv \triangle DEF \qquad \text { (SSS) } $$ \vfill \columnbreak \begin{center} \begin{tikzpicture}[scale=1] \coordinate[label=right:C] (A) at (2,0); \coordinate[label=below left:B] (B) at (-2,-1); \coordinate[label=above left:A] (C) at (-2,1); \draw[line width=1pt] (A) --(C)node[sloped,midway]{\(|\)}--(B)node[sloped,midway]{\(|||\)}--(A)node[sloped,midway]{\(||\)}; \end{tikzpicture}\\ \vspace{-0.4in} \begin{tikzpicture}[scale=1] \coordinate[label=left:F] (A) at (-2,0); \coordinate[label=below right:E] (B) at (2,-1); \coordinate[label=above:D] (C) at (2,1); \draw[line width=1pt] (A) --(C)node[sloped,midway]{\(|\)}--(B)node[sloped,midway]{\(|||\)}--(A)node[sloped,midway]{\(||\)}; \end{tikzpicture} \end{center} \end{multicols} \begin{multicols}{2} \(\triangle A B C \equiv \triangle D E F\)\\ since two corresponding sides and the included angle are equal $$ \text { i.e } \triangle A B C \equiv \triangle D E F\qquad \text { (SAS)} $$ \vfill \columnbreak \begin{center} \begin{tikzpicture}[scale=1] \coordinate[label=below right:C] (A) at (1.5,-1); \coordinate[label=below left:A] (B) at (-1.5,-1); \coordinate[label=above:B] (C) at (0,1); \draw[line width=1pt] (A) --(C)node[sloped,midway]{}--(B)node[sloped,midway]{\(|\)}--(A)node[sloped,midway]{\(||\)}; \pic [draw=black,line width=1pt,angle radius=0.6cm,angle eccentricity=1,""] {angle=A--B--C}; \begin{scope}[shift=(B)] \path (0:0.6) arc (0:50:0.6) node[midway,sloped] {\(|\)}; \end{scope} \end{tikzpicture} \begin{tikzpicture}[scale=1] \coordinate[label=below right:F] (A) at (1.5,-1); \coordinate[label=below left:D] (B) at (-1.5,-1); \coordinate[label=above:E] (C) at (0,1); \draw[line width=1pt] (A) --(C)node[sloped,midway]{}--(B)node[sloped,midway]{\(|\)}--(A)node[sloped,midway]{\(||\)}; \pic [draw=black,line width=1pt,angle radius=0.6cm,angle eccentricity=1,""] {angle=A--B--C}; \begin{scope}[shift=(B)] \path (0:0.6) arc (0:50:0.6) node[midway,sloped] {\(|\)}; \end{scope} \end{tikzpicture} \end{center} \end{multicols} \begin{multicols}{2} \(\triangle A B C \equiv \triangle D E F\)\\ since two angles and a corresponding side are equal. $$ \text { i.e } \triangle A B C \equiv \triangle D E F\qquad \text{ (AAS)} $$ \vfill \columnbreak \begin{center} \begin{tikzpicture}[scale=0.8] \coordinate[label=below right:B] (A) at (1.5,-1); \coordinate[label=below left:C] (B) at (-2.5,-1); \coordinate[label=above:A] (C) at (0,1); \draw[line width=1pt] (A) --(C)node[sloped,midway]{\(|\)}--(B)node[sloped,midway]{}--(A)node[sloped,midway]{}; \pic [draw=black,line width=1pt,angle radius=0.6cm,angle eccentricity=1,""] {angle=B--C--A}; \begin{scope}[shift=(C)] \path (-45:-0.7) arc (-45:215:-0.7) node[midway,sloped] {\(|\)}; \end{scope} \pic [draw=black,line width=1pt,angle radius=0.7cm,angle eccentricity=1,""] {angle=A--B--C}; \begin{scope}[shift=(B)] \path (0:0.8) arc (0:40:0.8) node[midway,sloped] {\(||\)}; \end{scope} \end{tikzpicture} \begin{tikzpicture}[scale=0.8] \coordinate[label=below right:E] (A) at (1.5,-1); \coordinate[label=below left:F] (B) at (-2.5,-1); \coordinate[label=above:D] (C) at (0,1); \draw[line width=1pt] (A) --(C)node[sloped,midway]{\(|\)}--(B)node[sloped,midway]{}--(A)node[sloped,midway]{}; \pic [draw=black,line width=1pt,angle radius=0.6cm,angle eccentricity=1,""] {angle=B--C--A}; \begin{scope}[shift=(C)] \path (-45:-0.7) arc (-45:215:-0.7) node[midway,sloped] {\(|\)}; \end{scope} \pic [draw=black,line width=1pt,angle radius=0.7cm,angle eccentricity=1,""] {angle=A--B--C}; \begin{scope}[shift=(B)] \path (0:0.8) arc (0:40:0.8) node[midway,sloped] {\(||\)}; \end{scope} \end{tikzpicture} \end{center} \end{multicols} \begin{multicols}{2} \(\triangle A B C \equiv \triangle D E F\)\\ since a right angle, a hypotenuse and\\ a corresponding side are equal. $$ \text { i.e. } \triangle A B C \equiv \triangle DEF \qquad \text{ (RHS)} $$ \vfill \columnbreak \begin{center} \begin{tikzpicture}[scale=0.8] \coordinate[label=below right:B] (A) at (1.5,-1); \coordinate[label=below left:C] (B) at (-1,-1); \coordinate[label=above:A] (C) at (1.5,2); \draw[line width=1pt] (A) --(C)node[sloped,midway]{}--(B)node[sloped,midway]{\(|\)}--(A)node[sloped,midway]{\(||\)}; \pic [draw=black,line width=1pt,angle radius=0.4cm,angle eccentricity=1,""] {right angle=B--A--C}; \end{tikzpicture} \begin{tikzpicture}[scale=0.8] \coordinate[label=below right:E] (A) at (1.5,-1); \coordinate[label=below left:F] (B) at (-1,-1); \coordinate[label=above:D] (C) at (1.5,2); \draw[line width=1pt] (A) --(C)node[sloped,midway]{}--(B)node[sloped,midway]{\(|\)}--(A)node[sloped,midway]{\(||\)}; \pic [draw=black,line width=1pt,angle radius=0.4cm,angle eccentricity=1,""] {right angle=B--A--C}; \end{tikzpicture} \end{center} \end{multicols}](/media/cyafuhsk/32393.png)
NSW Y8 Maths Congruent Figures Tests for Congruent Triangles
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