document.write( "Question 206813: If two altitudes of a triangle are equal , prove that the triangle is an isosceles triangle . \n" ); document.write( "
Algebra.Com's Answer #156450 by RAY100(1637)\"\" \"About 
You can put this solution on YOUR website!
altitudes are the same,,,,,,,,,,,,,,,given
\n" ); document.write( ".
\n" ); document.write( "Altitudes are perpendicular to a side,
\n" ); document.write( "therefore resultant triangles are rt triangles,,,,,,,,def altitude & def rt triangle
\n" ); document.write( ".
\n" ); document.write( "{ 2 sketches might help, isosceles triangles with altitudes to each equal side)
\n" ); document.write( ".
\n" ); document.write( "Base of the triangles are equal, ,,,,,,,,,,,same side
\n" ); document.write( ".
\n" ); document.write( "Triangles created by altitudes and common base
\n" ); document.write( "are congruent,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,by HL( hypotenuse leg)
\n" ); document.write( ".
\n" ); document.write( "Therefore, side of each triangle, bisected by the altitude
\n" ); document.write( "are equal, and base angles are equal,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,by CPCTC
\n" ); document.write( ".
\n" ); document.write( "Therefore, triangles are isosceles,,,,,,,,,,by def of isosceles triangle
\n" ); document.write( ",,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,(2 angles equal) \n" ); document.write( "
\n" );