SOLUTION: Supply the reasons missing from the proof shown below given: line ab = line ac, angle BAD = angle CAD prove: line ad = line bc

Question 674344: Supply the reasons missing from the proof shown below
given: line ab = line ac, angle BAD = angle CAD prove: line ad = line bc
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
it appears that you have an isosceles triangle with an altitude dropping from vertex A to intersect with the line BC at D.
the isosceles triangle is ABC.
The altitude drops to intersect with line BC at D.
this forms 2 triangles.
they are triangle ABD and triangle ACD
you are given the line AB is congruent to line AC which is why the triangle ABC is isosceles.
you are given that angle BAD is congruent to angle CAD which means that the altitude AD is the bisector of angle BAC.
since triangle BAC is an isosceles triangle and side AB is congruent to side AC, this means that angle ABD is congruent to ACD.
this means that triangle ABD is congruent to triangle ABD by angle side angle (ASA).
this means that side AD is congruent to side BC because corresponding sides of congruent triangles are congruent.
my diagrm of your triangle is shown below:
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