document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195016>Question 1195016</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given a parallelogram □ABCD, with AD > AB.<BR>\n" );
document.write( "The bisector of ∠A intersects 𝐵𝐶 at G, and the bisector of ∠B intersects𝐴𝐷 at H.<BR>\n" );
document.write( "Prove that □ABGH is a rhombus. </SPAN>\n" );
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document.write( "Let P be the intersection of AG and BH.<br><BR>\n" );
document.write( "Angles A and B in the parallelogram are supplementary.  Angle BAP measure is half the measure of angle A; Angle ABP is half the measure of angle B; so angle APB is a right angle.<br><BR>\n" );
document.write( "That makes triangles BPA and BPG congruent by Angle-Side-Angle; so BG is congruent to AB.<br><BR>\n" );
document.write( "A similar argument makes AH congruent to AB, making ABGH a rhombus.<br><BR>\n" );
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