Question 969073
<pre>
&#8773;&#8741;&#8736;&#916;&#8765;&#8869;

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locate(-.1,4.4,A), locate(-3.3,.4,B), locate(0,-4,C), locate(3.1,.4,D),
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Given: rhombus ABCD, E is the midpoint of DF
PROVE: AD is congruent to BF

1.  AD&#8741;BC       Opposite sides of parallelogram ABCD are &#8773;
2. &#8736;A&#8773;&#8736;EBF     Corresponding angles, &#8741; lines AD,BC cut by transversal AF.
3. &#8736;A&#8773;&#8736;C       Opposite angles of parallelogram ABCD are &#8773;
4. &#8736;C&#8773;&#8736;EBF     Angles &#8773; same angle are &#8773; to each other, 2,3
5. EF&#8773;ED        Given that E is the midpoint of DF
6. AB&#8741;CD        Opposite sides of parallelogram ABCD are &#8773; 
7. AF&#8741;CD        AF is an extension of AB, 6 
8. &#8736;BFE&#8773;&#8736;CDE   Alternate interior angles,&#8741; lines AF,CD cut by transversal DF. 
9. &#916;EBF&#8773;&#916;ECD    AAS, 4,8,5
10. BF&#8773;CD       CPCT, 9
11. CD&#8773;AD       All sides of rhombus ABCD are &#8773;
12. AD&#8773;BF       Things &#8773; same thing are &#8773; to each other, 10,11

Edwin</pre>