document.write( "Question 397236: In triangle ABC, the measure of angle A=36 AB=22, and AC=12; in triangle DEF the measure of angle D=36, DE=44, and DF=24. Justify whether or not the triangles are similar. \n" ); document.write( "

Algebra.Com's Answer #281580 by MathLover1(20850) $\"\"$ $\"About$

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Triangles are similar if they have the same shape, but can be different sizes. \r
\n" ); document.write( "\n" ); document.write( "In your case triangle $\"ABC\"$ , the measure of angle $\"A=36\"$ , $\"+AB=22\"$ ,\r
\n" ); document.write( "\n" ); document.write( "and $\"AC=12\"$ ; \r
\n" ); document.write( "\n" ); document.write( "and in triangle $\"DEF\"$ the measure of angle $\"D=36\"$ , $\"DE=44\"$ , and \r
\n" ); document.write( "\n" ); document.write( " $\"DF=24\"$ . \r
\n" ); document.write( "\n" ); document.write( "as we can see:\r
\n" ); document.write( "\n" ); document.write( "1. $\"corresponding\"$ $\"+angles\"$ are the $\"same\"$ ; $\"A=D=36\"$ \r
\n" ); document.write( "\n" ); document.write( "2. $\"Corresponding\"$ $\"+sides\"$ are all in the $\"same\"$ $\"+proportion\"$ \r
\n" ); document.write( "\n" ); document.write( "Above, $\"DE\"$ is $\"twice\"$ the length of $\"AB\"$ . \r
\n" ); document.write( "\n" ); document.write( "Therefore, the other pairs of sides are also in that proportion. $\"DF\"$ is \r
\n" ); document.write( "\n" ); document.write( " $\"twice\"$ $\"AC\"$ and $\"BC\"$ is $\"twice\"$ $\"+EF\"$ . \r
\n" ); document.write( "\n" ); document.write( "Formally, in $\"two\"$ $\"+similar\"$ triangles $\"ABC\"$ and $\"DEF\"$ you have:\r
\n" ); document.write( "\n" ); document.write( " $\"DE%2FAB=DF%2FAC=BC%2FEF\"$ \r
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\n" ); document.write( "\n" ); document.write( "so, your triangles $\"are\"$ similar\r
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