document.write( "Question 1007637: Write a two column proof
\n" ); document.write( "Line segment AB IS congruent to line segment AC, angle BAD is congruent to angle CAD
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Algebra.Com's Answer #623574 by ikleyn(52780) $\"\"$ $\"About$

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\n" ); document.write( "Write a two column proof
\n" ); document.write( "Line segment AB IS congruent to line segment AC, angle BAD is congruent to angle CAD
\n" ); document.write( "Prove:line segment AD bisects line segment BC
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document.write( "This statement is usually formulated as the \r\n" );
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document.write( "Theorem. In an isosceles triangle, the angle bisector to the angle between congruent sides is the median. \r\n" );
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document.write( "See the lesson An altitude a median and an angle bisector in the isosceles triangle in this site.\r\n" );
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document.write( "Below is the proof from this lesson.\r\n" );
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document.write( "Figure 3 shows an isosceles triangle ABC with sides AB and AC of equal length.\r\n" );
document.write( "The segment AD is the bisector of the angle BAC opposite to the base BC.\r\n" );
document.write( "We need to prove that CD is the median of the triangle ABC.\r\n" );
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document.write( "Since AD is a bisector of the angle BAC, the angles BAD and CAD are congruent.\r\n" );
document.write( "Thus, the triangles ADB and ADC have the pair of congruent sides AB = AC, the common                      \r\n" );
document.write( "side AD and the congruent included angles BAD and CAD.\r\n" );
document.write( "Hence, these triangles are congruent, in accordance to the postulate P1 (SAS) of the triangle \r\n" );
document.write( "congruency (see the lesson  Congruence tests for triangles under the current topic in this site).\r\n" );
document.write( "It implies that the segments BD and CD are congruent. \r\n" );
document.write( "This means that the bisector of the angle ACB is the median. \r\n" );
document.write( "Thus, the statement is proved.\r\n" );
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document.write( "        Figure\r\n" );
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