document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191303>Question 1191303</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Complete the formal proof of the following theorem.<BR>\n" );
document.write( "The bisectors of two adjacent supplementary angles form a right angle.\r<BR>\n" );
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document.write( "There is a line and three rays. There are six labeled points and four labeled angles.<BR>\n" );
document.write( "Line A D is horizontal. B is on this line and between A and D.<BR>\n" );
document.write( "Ray B C goes up and to the right.<BR>\n" );
document.write( "Ray B F goes up and to the right. Point F is below and to the right of point C.<BR>\n" );
document.write( "Ray B E goes up and to the left.<BR>\n" );
document.write( "Angle A B E is labeled 1 and is marked with one arc.<BR>\n" );
document.write( "Angle C B E is labeled 2 and is marked with one arc.<BR>\n" );
document.write( "Angle C B F is labeled 3 and is marked with two arcs.<BR>\n" );
document.write( "Angle D B F is labeled 4 and is marked with two arcs.<BR>\n" );
document.write( "Given:	<BR>\n" );
document.write( "∠ABC is supplementary to ∠CBD.<BR>\n" );
document.write( "BE bisects ∠ABC.<BR>\n" );
document.write( "BF bisects ∠CBD.<BR>\n" );
document.write( "Prove:	∠EBF is a right angle.<BR>\n" );
document.write( "Statements	Reasons<BR>\n" );
document.write( "  1. <BR>\n" );
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document.write( "  1. Given<BR>\n" );
document.write( "  2. <BR>\n" );
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document.write( "  2. The sum of the measures of supplementary ∠s is 180°.<BR>\n" );
document.write( "  3. m∠ABC = m∠1 + m∠2; <BR>\n" );
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document.write( "  3. <BR>\n" );
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document.write( "  4. <BR>\n" );
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document.write( "  4. Substitution<BR>\n" );
document.write( "  5. <BR>\n" );
document.write( "BE bisects ∠ABC;<BR>\n" );
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document.write( "BF bisects ∠CBD.<BR>\n" );
document.write( "  5. <BR>\n" );
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document.write( "  6. <BR>\n" );
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document.write( "  6. If a ray bisects an ∠, then two ∠s of = measure are formed.<BR>\n" );
document.write( "  7. m∠2 + m∠2 + m∠3 + m∠3 = 180°	  7. <BR>\n" );
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document.write( "  8. <BR>\n" );
document.write( "2 · m∠2 + 2 · m∠3 = 180°<BR>\n" );
document.write( "  8. Combine like terms.<BR>\n" );
document.write( "  9. m∠2 + m∠3 = 90°	  9. <BR>\n" );
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document.write( "10. <BR>\n" );
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document.write( "10. Angle-Addition Postulate<BR>\n" );
document.write( "11. <BR>\n" );
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document.write( "11. Substitution<BR>\n" );
document.write( "12. <BR>\n" );
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document.write( "12. <BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849150 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=849150\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's the completed two-column proof:\r<BR>\n" );
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document.write( "**Given:**\r<BR>\n" );
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document.write( "∠ABC is supplementary to ∠CBD.\r<BR>\n" );
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document.write( "BE bisects ∠ABC.\r<BR>\n" );
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document.write( "BF bisects ∠CBD.\r<BR>\n" );
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document.write( "**Prove:**\r<BR>\n" );
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document.write( "∠EBF is a right angle.\r<BR>\n" );
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document.write( "| Statements | Reasons |<BR>\n" );
document.write( "|---|---|<BR>\n" );
document.write( "| 1. ∠ABC is supplementary to ∠CBD. | 1. Given |<BR>\n" );
document.write( "| 2. m∠ABC + m∠CBD = 180° | 2. The sum of the measures of supplementary ∠s is 180°. |<BR>\n" );
document.write( "| 3. m∠ABC = m∠1 + m∠2; m∠CBD = m∠3 + m∠4 | 3. Angle-Addition Postulate |<BR>\n" );
document.write( "| 4. m∠1 + m∠2 + m∠3 + m∠4 = 180° | 4. Substitution |<BR>\n" );
document.write( "| 5. BE bisects ∠ABC; BF bisects ∠CBD. | 5. Given |<BR>\n" );
document.write( "| 6. m∠1 = m∠2; m∠3 = m∠4 | 6. If a ray bisects an ∠, then two ∠s of = measure are formed. |<BR>\n" );
document.write( "| 7. m∠2 + m∠2 + m∠3 + m∠3 = 180° | 7. Substitution |<BR>\n" );
document.write( "| 8. 2 · m∠2 + 2 · m∠3 = 180° | 8. Combine like terms. |<BR>\n" );
document.write( "| 9. m∠2 + m∠3 = 90° | 9. Division Property of Equality |<BR>\n" );
document.write( "| 10. m∠EBF = m∠2 + m∠3 | 10. Angle-Addition Postulate |<BR>\n" );
document.write( "| 11. m∠EBF = 90° | 11. Substitution |<BR>\n" );
document.write( "| 12. ∠EBF is a right angle. | 12. Definition of a right angle |<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );