SOLUTION: Given: rhombus ABCD, E is the midpoint of DF PROVE: AD is congruent to BF

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Question 969073: Given: rhombus ABCD, E is the midpoint of DF
PROVE: AD is congruent to BF
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
≅∥∠Δ∽⊥



Given: rhombus ABCD, E is the midpoint of DF
PROVE: AD is congruent to BF

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

Edwin