document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=168787>Question 168787</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you solve this proof for me. I tried every thing and could not prove this triangle congruent.<BR>\n" );
document.write( "Given: DA is perpendicular to AB, DC is perpendicular to CB, and AB is congruent to CB. Prove: angle CBD is congruent to angle ABD<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #124440 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=124440\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> it looks like the triangles are congruent by the hypotenuse-leg postulate.<BR>\n" );
document.write( "that states:<BR>\n" );
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document.write( "The Hypotenuse-Leg Postulate is a rule that you can use with right triangles only.  This rule is considered a postulate because it is not based on any other rules, as the theorems discussed above have been.  It states if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.<BR>\n" );
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document.write( "based on the information you provided, i sketched the triangles.<BR>\n" );
document.write( "it appears that BD is common to both triangles.<BR>\n" );
document.write( "if you draw BD horizontal.<BR>\n" );
document.write( "then draw BC going up at about a 45 degree angle from BD (not necessarily the real angle - just used for drawing purposes).<BR>\n" );
document.write( "then draw BA going down at about a 45 degree angle from BD.<BR>\n" );
document.write( "connect C to D forming a right angle at C (given)<BR>\n" );
document.write( "connect A to D forming a right angle at A (given)<BR>\n" );
document.write( "you have 2 triangles adjacent to each other with a commo side of BD.<BR>\n" );
document.write( "angle BCD is right angle (given).<BR>\n" );
document.write( "angle BAD is right angle (given).<BR>\n" );
document.write( "BC congruent to BA (given).<BR>\n" );
document.write( "BD congruent to BD (same line segment)<BR>\n" );
document.write( "BA and BC are legs of their respective triangles (BCD ad BAD).<BR>\n" );
document.write( "BD is the hypotenuse of triangles BCD and BAD since it is opposite the 90 degree angle of each.<BR>\n" );
document.write( "that makes the hypotenuse leg postulate work.<BR>\n" );
document.write( "triangles are congruent.<BR>\n" );
document.write( "angle CBD is congruent to angle ABD (corresponding angles of congruent triangles are congruent).<BR>\n" );
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document.write( "information about right triangles being congruent was found at this website:<BR>\n" );
document.write( "http://library.thinkquest.org/20991/textonly/geo/crtri.html#LL\r<BR>\n" );
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