document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=682141>Question 682141</A>: <I><SPAN STYLE=\"word-break: break-all;\"> in triangle ABC, the altitudes to the side AB and AC are congruent. Prove that quadrilateral PBCQ is:<BR>\n" );
document.write( "a. trapezoid<BR>\n" );
document.write( "b. isosceles trapezoid </SPAN>\n" );
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document.write( "In triangle ABC, Altitude from B and C are equal with each other. hence we have:<BR>\n" );
document.write( "BQ = PC \r<BR>\n" );
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document.write( "now consider two triangle PBC and Triangle QCB <BR>\n" );
document.write( " we have <BPC = <CQB = 90 degree each, <BR>\n" );
document.write( "BC = CB    is the common sides. <BR>\n" );
document.write( "BQ = PC     given equal altitudes.\r<BR>\n" );
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document.write( "Hence by RHS rule , <BR>\n" );
document.write( "Triangle PBC is congruent to Triangle QCB.<BR>\n" );
document.write( "PB = QC  by ( CPCT )\r<BR>\n" );
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document.write( "also these two triangles are congruent then there height must be equal , hence we <BR>\n" );
document.write( "can say that they must lie between the parallel lines ( PQ and BC ) <BR>\n" );
document.write( "hence PBQC is the ISOSCELES Trapezoid  ( since PQ parallel BC and PB = QC  ) </SPAN>\n" );
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