document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177132>Question 1177132</A>: <I><SPAN STYLE=\"word-break: break-all;\"> given: triangle abc is scalene<BR>\n" );
document.write( "       altitudes ae,cd\r<BR>\n" );
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document.write( "prove: ae is not congruent to cd<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 #850515 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850515\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Given Information**\r<BR>\n" );
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document.write( "* Triangle ABC is scalene. This means that all three sides of the triangle have different lengths.<BR>\n" );
document.write( "* AE and CD are altitudes of triangle ABC. This means that AE is perpendicular to BC, and CD is perpendicular to AB.\r<BR>\n" );
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document.write( "**2. Assumption**\r<BR>\n" );
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document.write( "Let's assume, for the sake of contradiction, that AE is congruent to CD.\r<BR>\n" );
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document.write( "**3. Area of a Triangle**\r<BR>\n" );
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document.write( "The area of a triangle can be calculated as (1/2) * base * height.\r<BR>\n" );
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document.write( "**4. Applying the Area Formula**\r<BR>\n" );
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document.write( "* Area of triangle ABC using base BC and altitude AE: (1/2) * BC * AE<BR>\n" );
document.write( "* Area of triangle ABC using base AB and altitude CD: (1/2) * AB * CD\r<BR>\n" );
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document.write( "**5. Using the Assumption**\r<BR>\n" );
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document.write( "Since we assumed AE ≅ CD, we can substitute AE for CD in the area formulas:\r<BR>\n" );
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document.write( "* (1/2) * BC * AE = (1/2) * AB * AE\r<BR>\n" );
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document.write( "**6. Simplifying the Equation**\r<BR>\n" );
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document.write( "If we divide both sides of the equation by (1/2) * AE, we get:\r<BR>\n" );
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document.write( "* BC = AB\r<BR>\n" );
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document.write( "**7. Contradiction**\r<BR>\n" );
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document.write( "This result contradicts our given information that triangle ABC is scalene (meaning all sides have different lengths).\r<BR>\n" );
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document.write( "**8. Conclusion**\r<BR>\n" );
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document.write( "Therefore, our initial assumption that AE ≅ CD must be false. Hence, we have proven that AE is not congruent to CD. </SPAN>\n" );
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