Question 965887
<pre>
Given: Rhombus ABCD with diagonal AC
To prove: ACF bisects &#8736;BAD and &#8736;BCD  

{{{drawing(250,300,-3,3,-4,4,

triangle(0,3,-2,0,0,-3), triangle(0,3,2,0,0,-3),

locate(-2.2,.2,B), locate(2.1,.2,D), locate(-.1,3.4,A),locate(-.1,-3,C),
locate(-.3,2.3,1), locate(.2,2.3,2), locate(-.3,-2,3), locate(.1,-2,4) )}}}

 1. AB &#8773; CD            1. opposite sides of a parallelogram are congruent
 2. BC &#8773; AD            2. opposite sides of a parallelogram are congruent
 3. AC &#8773; AC            3. a line is congruent to itself.
 4. &#916;ABC &#8773; &#916;ADC        4. SSS 1,2,3
 5. &#8736;1 &#8773; &#8736;4            5. corresponding parts of congruent triangles.
 6. &#8736;3 &#8773; &#8736;2            6. corresponding parts of congruent triangles.
 7. AB &#8773; BC            7. definition of rhombus, all sides congruent.
 8. &#916;ABC is isosceles  8. two sides congruent, 7
 9. &#8736;1 &#8773; &#8736;3            9. base angles of an isosceles triangle
10. &#8736;1 &#8773; &#8736;2           10. things congruent to the same thing are equal 
                          to each other, 6,9 11. AC bisects &#8736;ABD   11. from 10
12. &#8736;3 &#8773; &#8736;4           12. things congruent to the same thing are equal
                          to each other, 5,9
13. AC bisects &#8736;BCD   13. from 12 

Edwin</pre>