document.write( "Question 938786: a triangle XYZ has vertices X (1,1), y(3,1) and Z(2,4). Show that the triangle is an equilateral triangle \n" ); document.write( "

Algebra.Com's Answer #571962 by MathLover1(20850) $\"\"$ $\"About$

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an equilateral triangle is a triangle in which $\"all\"$ $\"three\"$ $\"sides\"$ are $\"equal\"$ \r
\n" ); document.write( "\n" ); document.write( "if a triangle $\"XYZ\"$ has vertices \r
\n" ); document.write( "\n" ); document.write( " $\"X\"$ at ( $\"1\"$ , $\"1\"$ ),
\n" ); document.write( " $\"y\"$ at ( $\"3\"$ , $\"1\"$ ) and
\n" ); document.write( " $\"Z\"$ at ( $\"2\"$ , $\"4\"$ )\r
\n" ); document.write( "\n" ); document.write( "to show that the triangle is an equilateral triangle, show that the distance between each two points is same \r
\n" ); document.write( "\n" ); document.write( "use distance formula to find the length of the all three sides\r
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\n" ); document.write( "\n" ); document.write( " $\"XY=sqrt%28%283-1%29%5E2%2B%281-1%29%5E2%29+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"XY=sqrt%282%5E2%2B0%29+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"XY=sqrt%284%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"XY=2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"YZ=sqrt%28%282-3%29%5E2%2B%284-1%29%5E2%29\"$
\n" ); document.write( " $\"YZ=sqrt%28%28-1%29%5E2%2B%283%29%5E2%29\"$
\n" ); document.write( " $\"YZ=sqrt%281%2B9%29\"$
\n" ); document.write( " $\"YZ=sqrt%2810%29\"$
\n" ); document.write( " $\"YZ=3.162277660168379\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"XZ=sqrt%28%282-1%29%5E2%2B%284-1%29%5E2%29\"$
\n" ); document.write( " $\"XZ=sqrt%281%2B9%29\"$
\n" ); document.write( " $\"XZ=sqrt%2810%29\"$
\n" ); document.write( " $\"XZ=3.162277660168379\"$ \r
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\n" ); document.write( "\n" ); document.write( "As $\"YZ\"$ and $\"XZ+\"$ are equal,the triangle is an $\"isosceles\"$ triangle , and (by definition) an isosceles triangle is a triangle with (at $\"least\"$ ) two equal sides
\n" ); document.write( "
\n" ); document.write( "an $\"equilateral\"$ triangle is a triangle with with all sides equal
\n" ); document.write( "an $\"equilateral\"$ triangle is therefore a special case of an $\"isosceles\"$ triangle having not just two, but all three sides and angles equal
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