document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=377366>Question 377366</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello Geometry tutor, Please help me with my problem number 1.\r<BR>\n" );
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document.write( "Given: ZM is perpendicular to XY, angle XZM is congruent to angle YZM.<BR>\n" );
document.write( "Prove: triangle XZY is isosceles.\r<BR>\n" );
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document.write( "Thank you very much!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #268186 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=268186\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the point of intersection of XY and ZM be B.  Then from the given, Angle XBZ and Angle YBZ are right angles and supplementary. Hence triangle ZBX and triangle ZBY are right triangles. By the HA Theorem for right triangles, triangle ZBX and triangle ZBY are congruent, and so ZX is congruent to ZY.  Hence triangle YZX is an isosceles triangle. </SPAN>\n" );
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