document.write( "Question 389517: Hello.
\n" ); document.write( "We are learning Inequalities for Sides and Angles of a Triangle in class.\r
\n" ); document.write( "\n" ); document.write( "A question asks:
\n" ); document.write( "Suppose angle WXY = angle XYZ. Which angle or of XYZ or WXY has the greatest measure?\r
\n" ); document.write( "\n" ); document.write( "The answer the book gives is angle W. I am not sure why. Can someone please explain?\r
\n" ); document.write( "\n" ); document.write( "Thanks.\r
\n" ); document.write( "\n" ); document.write( "\"Photobucket\" \n" ); document.write( "
Algebra.Com's Answer #276057 by Edwin McCravy(20063)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\r\n" );
document.write( "The other tutor used trigonometry, but that is not what you\r\n" );
document.write( "are studying here.  This is geometry, not trigonometry.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The figure is not drawn to scale at all.  We must redraw it more\r\n" );
document.write( "nearly to scale because it is necssary that YZ which has measure 17 \r\n" );
document.write( "to be drawn to look longer than WX, which has measure 12.  \r\n" );
document.write( "\r\n" );
document.write( "Here it is approximately to scale:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Angle W is the largest angle in triangle WXY because it's opposite the\r\n" );
document.write( "triangle's longest side XY.\r\n" );
document.write( "\r\n" );
document.write( "Angle XYZ is the largest angle in triangle XYZ because it is opposite the\r\n" );
document.write( "triangle's longest side.\r\n" );
document.write( "\r\n" );
document.write( "Therefore the largest of the six angles in both triangles is either\r\n" );
document.write( "angle W Or angle XYZ.\r\n" );
document.write( "\r\n" );
document.write( "Since angle WXY = angle XYZ, we can construct a triangle\r\n" );
document.write( "that's congruent to triangle WXY.\r\n" );
document.write( "\r\n" );
document.write( "We can locate point P on YZ, such that YP has measure 12, same as WX.\r\n" );
document.write( "And then draw XP. [This is why we had to redraw the figure because if\r\n" );
document.write( "you used the drawing at the top you would have to extend YZ.]\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now triangle PYX is congruent to triangle WXY by Side-angle-side.\r\n" );
document.write( "\r\n" );
document.write( "Therefore the green line XP has the same measure as WY, or 14.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now we see that Angle XPY is greater than angle XYP because\r\n" );
document.write( "in triangle XPY, Angle XPY is opposite a side of measure 15\r\n" );
document.write( "and XYP is opposite a side of measure only 14.\r\n" );
document.write( "\r\n" );
document.write( "Since Angle XPY has the same measure as angle W, angle W is the\r\n" );
document.write( "greatest interior angle in either triangle WXY or triangle XYZ.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );