document.write( "Question 674344: Supply the reasons missing from the proof shown below
\n" ); document.write( "given: line ab = line ac, angle BAD = angle CAD prove: line ad = line bc \n" ); document.write( "

Algebra.Com's Answer #419189 by Theo(13342) $\"\"$ $\"About$

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it appears that you have an isosceles triangle with an altitude dropping from vertex A to intersect with the line BC at D.
\n" ); document.write( "the isosceles triangle is ABC.
\n" ); document.write( "The altitude drops to intersect with line BC at D.
\n" ); document.write( "this forms 2 triangles.
\n" ); document.write( "they are triangle ABD and triangle ACD
\n" ); document.write( "you are given the line AB is congruent to line AC which is why the triangle ABC is isosceles.
\n" ); document.write( "you are given that angle BAD is congruent to angle CAD which means that the altitude AD is the bisector of angle BAC.
\n" ); document.write( "since triangle BAC is an isosceles triangle and side AB is congruent to side AC, this means that angle ABD is congruent to ACD.
\n" ); document.write( "this means that triangle ABD is congruent to triangle ABD by angle side angle (ASA).
\n" ); document.write( "this means that side AD is congruent to side BC because corresponding sides of congruent triangles are congruent.
\n" ); document.write( "my diagrm of your triangle is shown below:
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