Question 364316
line DB bisects < ADC and line BD bisects < ABC Prove: triangle ABD is congruent to triangle CBD
<pre>

{{{drawing(400,2000/7,-7,7,-5,5,

triangle(-6,0,0,4,6,0), triangle(-6,0,0,-4,6,0),

arc(-5,0,5,-5,0,45), arc(-5,0,4,-4,315,360),

arc(5,0,5,-5,135,180), arc(5,0,4,-4,180,225)

arc(5,0,5.5,-5.5,135,180), arc(5,0,4.5,-4.5,180,225)

locate(-6.5,0,B), locate(0,4.6,A), locate(0,-4,C), locate(6,0,D) 

 )}}} 

Here's an outline.  You can supply a 2-line proof

Angle ABD is congruent to angle DBC because BD bisects < ABC

DB and DB are congruent

Angle ADB is congruent to angle CDB because DB bisects < ADC

triangle ABD is congruent to triangle CBD by ASA (angle-side-angle)
Edwin</pre>