\r\n" );
document.write( "If the black triangle below is isosceles, and the vertices of the green\r\n" );
document.write( "triangle are the midpoints of the sides of the black triangle, that the\r\n" );
document.write( "green triangle is also isosceled:\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Since the black triangle is isosceles we can let it be triangle PQR,\r\n" );
document.write( "where the vertices are P(0,b), Q(-a,0), and R(a,0), where a and b are\r\n" );
document.write( "both positive numbers:\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Now we will let S, T. and U be the midpoints respectively of\r\n" );
document.write( "PQ, PR and QR.\r\n" );
document.write( "\r\n" );
document.write( "We will use the midpoint formula to find the coordinates of S,T, and U:\r\n" );
document.write( "\r\n" );
document.write( "For S:\r\n" );
document.write( "Midpoint =
\r\n" );
document.write( "Midpoint of PQ = S
\r\n" );
document.write( "Midpoint of PQ = S
\r\n" );
document.write( "\r\n" );
document.write( "For T:\r\n" );
document.write( "Midpoint =
\r\n" );
document.write( "Midpoint of PR = T
\r\n" );
document.write( "Midpoint of PR = T
\r\n" );
document.write( "\r\n" );
document.write( "For U:\r\n" );
document.write( "Midpoint =
\r\n" );
document.write( "Midpoint of QR = U
\r\n" );
document.write( "Midpoint of QR = U(0,0) \r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Now all we need is to show that US = UT.\r\n" );
document.write( "\r\n" );
document.write( "We will use the distance tance formula to show that:\r\n" );
document.write( "\r\n" );
document.write( " d =
\r\n" );
document.write( "SU =
\r\n" );
document.write( "SU =
\r\n" );
document.write( "SU =
\r\n" );
document.write( "SU =
\r\n" );
document.write( "SU =
\r\n" );
document.write( "SU =
\r\n" );
document.write( "\r\n" );
document.write( " d =
\r\n" );
document.write( "TU =
\r\n" );
document.write( "TU =
\r\n" );
document.write( "TU =
\r\n" );
document.write( "TU =
\r\n" );
document.write( "TU =
\r\n" );
document.write( "TU =
\r\n" );
document.write( "\r\n" );
document.write( "So SU = TU and therefore triangle STU is isosceles.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" );
document.write( "